with a Special Section on the Timex/Sinclair 2000 THE ESSENTIAL GUIDE TÜ TIMEX/SINCLAIR HOME COMPUTERS ! The Only Book You'll Ever Need to Become an | Expert at the Timex/Sinclair 1000 and 2000 li ЖДД ЕТП : f "d cundo 3H YIVIINIS/KIWIL ñ. E 1 ' Е E МУГ ы ЕК ie L E S M 4 % 5 | а \ ( ' “ [| | li ( ү ж | я , TY 7 ` ` | E 4 є d] j = у | et Ties | А | E ч т, d x I ^ ; s a | - EN А Gs > i E»: "A "v 4 y "4p". THE ESSENTIAL GUIDE TO TIMEX/SINCLAIR HOME COMPUTERS The Only Book You'll Ever Need to Become an Expert at the Timex/Sinclair 1000 and 2000 by PETER MORSE, IAN ADAMSON BEN ANREP and BRIAN HANCOCK A TOUCHSTONE BOOK Published by Simon & Schuster, Inc. NEW YORK We are grateful to Sinclair Research for their cooperation This book was published in England under the title The Century Computer Programming Course Copyright © 1983 by Eosoft All rights reserved including the right of reproduction in whole or in part in any form A Touchstone Book Published by Simon & Schuster, Inc. Simon & Schuster Building Rockefeller Center 1230 Avenue of the Americas New York, New York 10020 Published by arrangement with Century Publishing Company, England TOUCHSTONE and colophon are registered trademarks of Simon & Schuster, Inc. Manufactured in the United States of America 10 98 765 43 2 1 Pbk. Library of Congress Cataloging in Publication Data Main entry under title: The Essential guide to Timex/Sinclair home computers. (A Touchstone book) British ed. published as: The century computer programming course. 1. Timex 1000 (Computer)—Programming. 2. Timex Sinclair 2000 (Computer)—Programming. 3. Basic (Computer program language) I. Morse, Peter (Peter L. R.) II. Title. QA76.8.T48E77 1983 001.64'2 83-9090 ISBN 0-671-47069-8 Pbk. IMPORTANT NOTE FOR ALL READERS This book uses the Sinclair version of single keystroke BASIC as featured on the ZX81 and Spectrum microcomputers. In the States the ZX81 has been marketed as the Timex/Sinclair 1000 and the Spectrum is known as the Timex/Sinclair 2000. American readers should note that throughout the text we refer to these machines by their UK names. There are a few minor differences between the UK version of the ZX81 and the US TS 1000. The first is that the TS 1000 has more ‘on board’ memory (2k) than its UK equivalent. However, this is still insufficient for the scope of this text, and the majority of the programs occurring in the book will require a 16k RAM pack. The second difference is that two keys, which do exactly the same thing, are labelled differently. Thus, NEWLINE and ENTER are equivalent on the ZX81 and the TS 1000, as are RUBOUT and DELETE. On each occasion that these commands occur in the text, readers will find either NEWLINE (ENTER) or RUBOUT (DELETE). For the sake of clarity we have used the ZX81/TS 1000 version of BASIC as the foundation of the book, and have noted those instances where Spectrum (TS 2000) BASIC differs from that used by the ZX81 (TS 1000). Functions and commands exclusive to the Spectrum (TS 2000) BASIC superset are fully explained at the end of the book (Units W2 and W3). In short, the book has been designed to enable its readers to learn how to program using any of the Sinclair machines. Users of the Spectrum should note that all programs are listed in capital letters throughout. To get program results and listings that look identical to those given here the capital letter (CAPS) mode must be used on the Spectrum for all letters input or printed. The first two Units of Part One deal only with the ZX81. The Spectrum user should read instead Unit W1 (page 439) of the Spectrum dedicated Section which forms Part Five of this text. 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CONTENTS page Introduction xiii PART ONE FIRST STEPS xvii SECTIONA THEZX81 MICROCOMPUTER SYSTEM l А! 7Х81 System Description A2 Function of Components + SECTIONB GETTING TO KNOW THE ZX81 7 ВІ Connecting Up B2 Тһе Keyboard 9 B3 Cursors 10 B4 ‘The Different Character Types 12 SECTION C BASIC BASIC 19 СІ Тһе BASIC Language 19 C2 А Simple Program 19 СЗ AStatement 20 C4 Statement Numbers 20 C5 Instructions 21 C6 Numeric Variables 21 C7 Strings and String Variables 23 C8 Operators and Operands 24 C9 Format of Statements 24 C10 Keying in a Statement 24 C11 Correcting Errors 26 C12 Commands 27 C13 Editing the Program 28 C14 Listing a Program on the Screen 29 C15 Running the Program 29 C16 Error Messages 31 C17 How the Program Works 32 C18 Naming the Program 33 SECTIOND SAVING, LOADING AND LISTING PROGRAMS 35 D1 Saving the Program on Cassette Tape 35 D2 Deleting the Program from Memory 38 D3 Loading the Program from Cassette Tape 40 vii D4 D5 Listing the Program on the Printer Program Libraries and Directories SECTIONE IMPROVING THE PROGRAM El Е2 ЕЗ Е4 Е5 E6 Adding Comments Using the Print Statement Adding a Loop Stopping the Program Testing for a Condition Final Edit and Saving SECTION F A GAME INTERLUDE El F2 The Program Library A Game to Key In PART TWO ESSENTIALS OF BASIC PROGRAMMING SECTION G PROGRAMMING METHODS I G1 G2 G3 G4 G5 G6 G7 G8 G9 G10 Programming Problem Analysis Structure Diagrams Classifying Program Modules Control Structures The Data Table Describe the Algorithm The Pseudocode Description Flowcharts Testing the Algorithm SECTIONH CONTROL H1 H2 H3 H4 H5 H6 Control in Programs Condition Testing IF-THEN GOTO Instructions Decision Structures Logical Operators: AND/OR SECTIONI PRINTING I1 I2 PRINT/LPRINT Spacing Items on the Screen viii 57 43 44 46 46 46 47 48 49 51 53 53 53 59 59 60 63 65 67 70 72 73 74 84 86 86 86 87 88 89 96 99 99 100 ІЗ 14 РКІМТАТ Тһе Graphics Characters оп (һе ZX81 SECTION J ARITHMETIC AND FUNCTIONS Ji J2 J3 J4 JS J6 J7 18 19 Ј10 wil 112 113 Arithmetic Operations Priority Number The E Notation Rounding How Numbers are Handled Function List of Functions in Sinclair BASIC The Function Characters The Function Character Set The Standard Mathematical Functions Trigonometric Functions Special Functions SECTION K STRINGS K1 K2 K3 K4 K5 K6 K7 K8 K9 K10 K11 K12 Strings Quotes and Quote Image String Input Length of a String Null Strings String and String Array Variables String and String Array Dimension String and String Array Assignment Substrings and String Slices String Concatenation Comparing Strings Strings and Numbers SECTION L LOOPS L1 L2 L3 L4 L5 Loops Counters FOR-NEXT Loops Loops of Variable Length Nested Loops SECTIONM PLOTTING MI M2 PLOT and UNPLOT Graph Plotting IX 102 104 108 108 108 111 111 114 115 116 117 118 119 120 122 123 126 126 127 128 130 130 131 131 132 133 135 136 139 142 142 143 147 153 155 159 159 162 SECTIONN SUBROUTINES N1 N2 N3 N4 N5 N6 Subroutines Subroutine Example Nested Subroutines Recursive Subroutines Computed GOSUBs Subroutine Use: Example PART THREE ADVANCED BASIC PROGRAMMING SECTIONO PROGRAMMING METHODS II Ol O2 O3 O4 O5 SECTION P THE CHARACTER SET AND CODES Р1 P2 P3 P4 Resume Producing the Program Coding and Design Program Development The Complete Programming Method The ZX81 Character Set and Codes The Spectrum Character Set and Codes Characters CHR$ and CODE SECTION Q GRAPHICS O1 Q2 Q3 Q4 More Printing More Plotting Movement and Timing The Display File SECTION R LOGICAL OPERATIONS R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 Logical Values and Numeric Values Boolean Operators: The AND Operator The OR Operator The NOT Operator Conditional Operators Logical Operations on Conditional Expressions Multiple Logic on Conditions Logical Operations on Numbers Priority Logical Operations with Strings X 169 169 170 172 172 177 179 R11 Logical Operations Between Strings and Conditions R12 Logical Operations Between Numbers and Conditions R13 Applications of Logical Operators SECTIONS LISTS AND ARRAYS 51 Dimension S2 Index Variable S3 Lists 54 Examples of Lists S9 String Arrays S6 Two Dimensional Numeric Arrays 57 Multi dimensional Arrays S8 | Useof Arrays SECTION T SORTING, SEARCHING AND STORING ARRAYS T1 Searching and Sorting T2 Bubble Sort with Flag T3 Alphabetic Sort T4 Insertion Sort T5 ShellSort T6 Quick Sort T7 Index Sort T8 Linear Search T9 Binary Search T1Q Storing a List T11 Storing a String Array T12 Storing Data in Strings SECTION U THE COMPUTER MEMORY U1 Memory Organisation U2 PEEK and POKE ОЗ System Variables PART FOUR APPLICATIONS PROGRAMS AND GAMES SECTION V APPLICATIONS PROGRAMS V] Programming for Applications V2 Instructions and Input Checks V3 Example Programs V4 Games Programming xi 351 270 271 272 279 279 279 280 280 283 284 286 287 292 292 294 295 296 299 302 306 309 310 312 314 316 319 319 325 332 353 299 354 359 425 V5 Example Programs 426 PART FIVE COVERING THE WHOLE SPECTRUM 437 SECTIONW THESPECTRUM 439 W1 The Spectrum System and Keyboard 439 W2 Additional Spectrum BASIC Functions 456 W3 Graphics, Colour and Sound 466 APPENDICES 477 I Sinclair BASIC Summary 477 II Error Codes 483 HI ZX81 Character Codes by Keyboard Arrangement 487 ГУ Use of Cassette Tapes 491 V System Variables 493 VI Program Library 499 хи INTRODUCTION The central conviction behind this book is that programming computers to solve problems is essentially a language independent activity. This means that there is no reason why Sinclair BASIC should not be learnt in exactly the same way as other high level languages: that is, with the fundamentals of problem solving апа structured programming introduced at an early stage. For the majority of readers, Sinclair BASIC will be their first introduction to computing. We would like to think that many will use it as a stepping stone to more advanced study and application. Good problem solving and programming habits will make both applications programming in BASIC and learning a different structured language like PASCAL (which has a richer programming environment than BASIC), much easier. We are convinced that bad programming habits acquired early on are extremely difficult to throw off; thus, this book has been designed to introduce readers to the elements of computer programming in a systematic manner, with the emphasis on correct rather than merely adequate techniques. Although we intend the text to be a serious treatment of Sinclair BASIC, ав an introduction to computing it assumes по prior knowledge of computers and only a minimal understanding of mathematics. (Without the maths you will still be able to make your way through the book, but if you don’t know what SIN and COS are, you won’t be able to write programs using them!) Before all else, we intend to give readers a full introduction to the essential control and modular structures present in truly structured computer languages and the way in which they operate in Sinclair BASIC. Once again, we hope that with this behind them, readers will be able to go on to tackle more sophisticated computer languages with a clear understanding of the essentials of good programming in any language. This approach also ensures that the reader who stays with his Sinclair machine will be able to maximise its potential. As it runs on the world’s most popular microcomputers, there can be little doubt that Sinclair BASIC will become one of the most commonly used computer languages. This, coupled with the fact that more and more software is becoming available for the machines, makes it all the more important that users attain a sound understanding of the language. Most published programs in books and magazines have little in the way of documentation. Debugging them, normally a tedious and difficult task, becomes much easier if the techniques to do so are known. This book introduces readers to three main sets of computer rules: 1 The rules of using your computer system. 2 The rules of the Sinclair BASIC programming language. 3 The rules of problem solving and structured programming using Sinclair BASIC. xiii WHY DID WE WRITE THIS BOOK? The sheer availability of the Sinclair machines demands that they be treated seriously as a means of teaching progamming methods to a large number of people. The programmer of a personal computer must understand the characteristics of the machine, the high level language (in this case BASIC), by which it is used and controlled and the problem solving techniques to which it should be applied. The first rush of books on the Sinclair machines has been, to put it kindly, disappointing. Certainly none can be considered a serious text on Sinclair BASIC. We felt that a book was needed which gave the first time user a worthwhile home tutor on computing. So we decided to write one! WHO IS THE BOOK FOR? The book has been written for the home user or school user who has just bought a ZX81 or Spectrum and wants to learn how to program it from scratch. Experience has shown that most Sinclair users will buy more than one book on the subject of programming their machine. This book will clear up a few misunderstandings and confusions presented by other texts and will take you further into programming techniques. The text has also been designed as an aid to Sinclair BASIC programmers who are having trouble designing error free programs and are attempting some serious application. HOW IS THE BOOK STRUCTURED? As a self-study text, this book should be worked through with your computer in front of you, so that programs and examples can be keyed in as and when they arise. The book has twenty-three Sections and is divided into five Parts. Part 1: FIRST STEPS in which, after a brief introduction to the machine and system (the first two units are ZX81 specific, and Spectrum users should go immediately to the Spectrum specific units - W1 on page 439 - before returning to start the main text at Section C) you are told how to set it up correctly and start to write and run simple BASIC programs. Part 2: FUNDAMENTALS OF BASIC PROGRAMMING, which first introduces the reader to the fundamentals of problem solving and structured programming in BASIC. Тһе properties and implementation of important language CONTROL STRUCTURES - decisions, loops, and subroutines - are introduced, together with the use of arithmetic, functions, strings, and how to print and plot information on the screen. Part 3: ADVANCED BASIC PROGRAMMING contains further sections on programming methodology, as well as details of debugging, XIV testing and documenting programs. Interactive graphics is introduced, together with the use of logical operators. Lists and arrays and methods to sort and search them (vital subjects for applications programming) and a treatment of how the computer uses its memory are fully covered. Part 4: APPLICATIONS PROGRAMMING AND GAMES focuses the fundamental programming skills acquired in the earlier parts of the book in the study of specific examples, linked to some further discussion of programming technique. Part 5: COVERING THE WHOLE SPECTRUM is the portion of the book dedicated to the Spectrum. The first Unit of this Section, dealing with the Spectrum system and keyboard, replaces the ZX81 specific Sections A and B, since there are major differences in the arrangements of the two machines which require separate treatment. The two following Units in this Part of the book deal with additional features of the Spectrum not covered in the main text. It is intended that, after using the first Unit to acquaint him or herself with the Spectrum, the reader should defer reading these Units until the main body of the text has been worked through. For the Spectrum user, this starts at Section C. The book is detailed and thorough. Remember that programming is learned most effectively through experience. You should work through the text systematically using your computer. Key in each example in the text and run it. Some further programs to key in are available in Appendix VI. The exercises which appear at regular intervals throughout the book are meant to give you practice in programming methods and to further illustrate the function and application of the Sinclair BASIC language constructions. Attempt most of them, but don’t ever allow yourself to become discouraged. If you get stuck, go back through the relevant section again. We hope that you find learning BASIC programming with this book a successful, enjoyable and useful experience, and that the knowledge and programming skills obtained will be a step on the path to a more advanced use of your Spectrum or ZX81 for real applications and enjoyment. XV ІҢ $E ІН H dand pd ІН pur tips SMS, AN Cree iwi S4 Шаға Mad өш do^ > eet 7 bonua «canted ‘Hee Kets? volut. йй ay aint arrests ПОЛО grieved bets) tao tari ed gn deabus nord бы? чый oe sura age Tiber: iron «М. заз (eo m £ -GA < ihe и ж ула % «©.» {кулан Ya кзжсжттер bgr там, ъз + Min Pí Г ұлығ | nus зыр“ iai паз 1 D нұйуі, АТИ PART ONE FIRST STEPS Important Note: The first two units of this part are specific to the ZX81. Spectrum users should ignore these pages and directly GOTO the first Spectrum specific section (W1 on page 439) before returning to the main text (Section C on page 19). Зин ERAS LI рч SECTION A: ZX81 MICROCOMPUTER SYSTEM A1: ZX81 Description We assume you have in front of you the components of your ZX81 computer system. It consists of: 1 Тһе ZX81 microcomputer with its touch-sensitive keyboard. 2 The Sinclair 16k RAM pack (Random Access Memory) or a RAM pack of at least 16k produced by one of the other manufacturers for the ZX81. 3 The ZX power supply, with a lead and plug, for connection to the a.c. power supply, and the lead, ending in a jack-plug, to connect the power supply unit to the ZX81. 4 The ZX printer and its connector socket. A domestic UHF ТУ set to be used as a TV monitor. 6 А mono cassette recorder, with power supply lead if not battery powered. The aerial cable which connects the ZX81 to the TV monitor. 8 A pair of cassette recorder leads fitted with 3.5mm jack-plugs оп each end. сл I These components make up a complete system. As far as this text is concerned, the least crucial component is the printer. Without it you can simply ignore the printer-related portions, and will be able to work through the book and learn the BASIC programming techniques just as well. However, it is extremely useful to have a printer both for hard- copy printouts of results, and more importantly for program listings for documentation purposes. There are a large number of ‘add-ons’ and accessories available for the ZX81. None of these are of any interest as far as this book is concerned, and most should be considered only when you have absorbed the text and are going to write programs for specific purposes, which might require the facilities provided by some of these units. A noteworthy exception is a workstation to hold the components of the system securely. There are types available which have on/off switches for the d.c. power supply from the power supply unit, which saves a lot of plug pulling and re-insertion, since pulling the power plug out of the ZX81 is the only way to re-set the computer if it ‘crashes’ (i.e. will not respond to keyboard commands). What ¿s vital is enough memory. RAM memory is measured by kilobytes (‘k’). The basic ZX81 has only 1k of RAM built in (2k on the Timex/Sinclair 1000), and, without an add-on, RAM memory has very little space available for programs. Computers are essentially devices which store and manipulate data, and since programs, data, and the manipulations all take up memory space, an add-on RAM 1 Figure 1 ZX81 SYSTEM DIAGRAM ас. household power supply AERIAL TV MONITOR SOCKET POWER EAR а CASSETTE SUPPLY МІС | RECORDER NOTE: U.S. USERS MAY HAVE ANTENNAE ON/OFF SWITCH FITTED IN AERIAL LEAD, SHOWN AS DOTTED BOX IN DIAGRAM. memory is needed. RAM memory of up to 48k is available for the ZX81, but 16k is more than enough for our purposes. Independently produced RAM packs are usually just as good as those produced by Sinclair. The cassette recorder should be mono, since stereo tape deck recording heads can cause problems, even used on one channel only. The cheaper recorders work somewhat better (due to the less sophisticated audio circuits being better for handling the crude form of the computer’s signals) than more expensive ones, but try to get one with a tape counter, as finding programs without one can be irritatingly time consuming. You should always use the same recorder, as problems can be encountered when playing back tapes recorded on a different machine. Battery-operated recorders actually avoid some potential problems, but must always have good batteries, to keep tape 2 speed constant. The cheapest solution to this in the long term (especially since if you're not sure about the state of the batteries you have to put in new ones) is to buy nickel-cadmium batteries and a charging unit. All recorders have automatic level controls for recording, but some cause problems with their continual variation around the correct level (‘hunting’). Get a model that has been shown to be compatible with the Sinclair computers. Having a TV for exclusive use with your computer system 1s a good idea, to avoid having to unplug and move around elements of your system (it also avoids arguments with non-computing members of the family!). Some problems can interfere with the operation of your computer (leaving to one side things like spilling coffee on it or otherwise abusing it!). The first is overheating. After the computer has been on for some time, it may heat up to such an extent that it ‘whites out’ and wipes out the program you have just finished, except for that last line. This is very irritating, to say the least. Some ZX81s seem to suffer from this more than others. If it is a persistent problem, it can be helped by placing a fairly hefty chunk of metal on top of the case to radiate heat away more effectively. It should be approximately 3 x 2 inches and 0.5 inch deep, have a flat surface to sit on the ZX81 case, and should be placed on the case, above the keyboard, on the left-hand side of the case. lhe corollary to this problem is that you should SAVE a long program being developed or keyed in at intervals, and/or take listings from the printer, to avoid a total loss if you do get a white out. The same problem can also be caused by two other factors, and this procedure will protect against the worst results from these problems as well. The first is that household power supplies are sometimes interrupted, or occasionally have brief large voltage fluctuations. Computers are sensitive to such things, and a crash may be caused. Other than buying a stabiliser which will continue to supply power during such an interruption (of very short duration, but computers work fast!) we cannot protect against a.c. supply fluctuations, but similar results can sometimes be caused by appliances connected to the same local power circuit switching on and off, and this should be investigated if the problem is frequent. The other main source of problems is the connector to the RAM pack and printer via the edge connectors at the back of the ZX81. Movement can be caused in this connector by flexing the system whilst keying in programs. This can be minimised by always pushing the connectors home firmly before switching on, but a better solution is to attach the components to a board, fixing them down to a suitably rigid base with ‘Blu-Tack’ or the double sided adhesive pads that are now available. Fix the printer down as well- the process of tearing off printout can move printer and connector if you are not careful. Note that the method of fixing cannot be permanent, which is why Blu- Tack 3 or a similar plastic fixative is recommended. The edge connectors themselves are gold plated, but they connect to the printed circuit board edges which may become oxidised, causing circuit problems (not necessarily white-outs or crashes — the keyboard may cease to work, or the printer miss lines, for example). Proprietary (non-abrasive) contact cleaners should be used to ensure clean contacts. Other than the problems above, the only maintenance that should be needed is the brushing away of the dust that accumulates in the printer from the burnt-off particles of paper. After removing the paper holder, use a soft small brush (e.g. a small paint brush) to clear away the dust. Pay particular attention to the slot in which the electrode runs, but if, as sometimes happens, the electrode is visible, do not disturb it. (The electrode is a small piece of wire which is normally not visible, but if BREAK has been used it can be left in the middle of the printer slot.) A2: Function of Components This is a programming text, not a manual on computer architecture or computer science. However, we thought it might be useful to provide you with a brief rundown of the functions of each of the components of your microcomputer system. Device Function ZX81 computer board Data processing and control of (inside case) information handling. Input from keyboard or cassette. Output to TV screen and printer. Keyboard Input of information. Programs, data and commands are keyed in. On-line control. TV set Used as V.D.U. (visual display unit) monitor. Provides on-line output of information — visual display of programs, results (data, graphs, pictures) and control commands. Cassette recorder Off-line storage of information. Program data are stored (written) as coded electromagnetic impulses on cassette tapes. They can be played back (loaded) at any time for use again. The computer reads the data from the tape. ZX printer Output device, to provide a permanent printed record of the screen display, program listings or information in the computer memory. Prints on electrosensitive paper. 16k RAM pack Add-on memory enabling large Power Cables programs to be stored and run. K stands for kilobyte. One byte is eight 22/5, which аге the binary digits (0 and 1, represented by on-off switches in the computer) computers work with. A kilobyte is roughly 1000 bytes, hence the name. (It is actually 29, 1024). supply Supplies the d.c. current (9 volts at 1.2 amps) to run the computer, RAM pack and printer, from the household power supply. To interconnect the devices which make up the system. The printer uses the same socket as the memory pack and has an extension socket to allow this. The printed circuit board inside the ZX81 holds and connects the IC (integrated circuit) microchips which provide the computing facilities. These 1 are: Z80A CPU (Central Processing Unit) microprocessor chip which is the heart of the system. It is used in many other microcomputers, and performs the arithmetic manipulations. ROM (Read Only Memory) chip holds the 8k BASIC interpreter which translates BASIC instructions into the machine code instructions that the Z80A operates with. The data in this chip is fixed, hence the name, and also stable — it remains when the power is switched off. 3 RAM (Random Access Memory) chip provides a 1k* memory store. When the memory pack is fitted it blocks off this memory and substitutes its own 16k of memory. This memory is volatile — the data is stored as electrical impulses and is lost When the power is switched off. This memory stores the BASIC programs, the values of variables (including some system variables that the computer uses to organise its own affairs), a memory picture of the ТУ screen display, and the stacks which hold the numbers whilst they are being manipulated. This is covered in more detail in Section U. 4 The Logic chip co-ordinates the operation of the other chips. Also mounted on the board are: the stabiliser for the 5 volt supply the computer takes from the power supply, the TV signal modulator and the sockets for the connecting cables to the ГУ and cassette recorder. *2k on the TS 1006. SECTION B: GETTING TO KNOW THE ZX81 B1: Connecting Up 1 Lay out the ZX81 system devices on your work area as оп page 2. It is far better to have an area where the system can be set up permanently. Failing this, a board can be used to mount the components. Place the a.c. power supply plugs of the power supply, ТУ and tape recorder next to the sockets. A plug board with multiple sockets mounted on it is better than an extension socket fitting. Connect the printer socket into the 23 pin edge connector at the back of the ZX81. Get the slot in the ZX81 board and the block in the printer socket aligned and push in gently but firmly. Connect the 16k RAM pack socket into the extension connector at the back of the printer socket in the same way. This is better done with the ZX81 flat on the table to avoid too much stress on the connectors, which might occur if you are holding up the LAB, With both connectors inserted, push the RAM pack firmly in to ensure the connectors are fully seated home. Connect the power supply cable into the socket marked DC on the left-hand side of the ZX81. Connect one end of the twin jack-plug leads, placing one jack- plug into each of the MIC and EAR sockets on the cassette recorder. Place the other jack-plugs into the ZX81 sockets. It is very useful to have the EAR and MIC sockets marked on the top of the ZX81 case, where the marks can be seen. Use sticky labels of some type to mark which is which, and also the exact centre of the plug socket. This will save much probing of sockets (there are no guides to ensure you get the socket) and peering at the markings on the side of the ZX81, which are scarcely visible when the ZX81 is flat on a surface. The yellow banded plugs should go to both MIC sockets. You can also mark the other jack-plug with E or EAR as a helpful aid. Push the jack-plugs gently in, making sure the tips are in the sockets (which has to be done by feel) until a resistance is felt, then push until they click into place. Waggle them slightly to ensure they are well-seated. Connect the aerial lead into the ТУ aerial socket at the rear of the TV and into the TV socket on the ZX81. A slight twisting motion may be needed if the fit is tight. US Users will find that the TV connects to the antenna lead with standard terminals, and an antenna ON/OFF switch is fitted between the antenna lead and the antenna lead that plugs into the 7 Timex/Sinclair 1000 version of the ZX81. This switch must of course be ON. Straighten the interconnecting cables on your work area at this point. Make sure that the cassette leads are not in contact with any a.c. power leads. SWITCHING ON оомо C 10 11 12 13 Ensure that the TV receiver is off and that no cassette recorder keys are depressed. Plug the power supply, TV, and cassette recorder plugs into the a.c. power supply. Switch on the a.c. power sockets (if they have switches). There are no ON/OFF switches on the ZX81 or on most cassette recorders - they are now powered up. Switch on the TV. Turn the volume control on the ТУ to zero. Turn the brightness control to MAXIMUM. Turn the contrast control to MINIMUM. Tune in the TV. With a rotary tuning control, turn to channel 36. Otherwise select a channel, using the pushbutton or other channel select switch, and tune this channel in. When the ГУ is at the right setting, a small black square with a white K inset appears. This is the K-cursor, and appears on the bottom left- hand side of the screen. U.S. Users should note that the Timex/Sinclair 1000 version of the ZX81 has a channel select switch for Channel 1 or Channel 2 fitted underneath the case. Choose whichever channel is not transmitting in your area, and select this channel on the TV and the computer. Adjust the tuning, brightness and contrast until the cursor is distinct, and the white K clear. Check that the cassette recorder keys function. Insert a blank cassette, and try all the controls. Insert a roll of silver printing paper into the printer and press the button on the right-hand side of the printer to feed some paper through. Check the paper does not rub on either side of the printer as it comes through. Press the key and then the [NEWLINE (ENTER) | key. The printer will start to copy what is on the screen. About 3 inches of paper will be fed through. There will be nothing printed on it as there is nothing on the screen. A message 0/0 will appear at the bottom of the screen. N.B. The bottom two lines of the screen are never printed and are used for keying in program lines and commands. These program lines, when correct, are transferred into an area of 8 memory reserved for the programs by pressing the NEWLINE (ENTER) key. The program lines will then appear on the printer when the COPY command is given. 14 Press characters at random on the keyboard. They will appear at the bottom of the screen. Press and [EDIT | keys together to clear the screen. 15 If the cursor will not appear on the screen switch off the power supply and adjust the 16k RAM pack and printer connections. Switch on the power supply again and retune the TV. N.B. Never adjust or pull out the RAM pack when the power supply is ON, you may damage it. 16 Other components failing to work will probably be caused by plugs not switched on, or fuses blown. Alternatively, it could be that some connections are not being properly made. You should remove and re-insert Jack-plugs and connectors. 17 On leaving your computer: a Leave it connected up b Switch OFF a.c. power supply plugs and TV c Disconnect plugs from sockets. B2: The Keyboard The ZX81 keyboard has 40 touch sensitive keys arranged in 4 rows of 10 keys. At first sight it looks like a typewriter keyboard, but a closer look reveals that some keys have five functions or characters written on them. In fact: Six different characters can be obtained from some keys! The keyboard contains: (1) The digits 0 to 9 (2) The letters of the alphabet printed in upper case (3) The complete BASIC language — instructions — commands — arithmetic, conditional and logical operators — arithmetic functions (4) Grammatical signs and symbols (5) Special control keys (6) Graphics symbols These are all called characters. Notice that words like PRINT, RUN, SLOW, LET, INKEY$ are 9 written on the keys and are printed on the screen when we press that key in the correct mode. The facility of complete words in the BASIC language being printed at the press of a single key is called SINGLE KEYSTROKE BASIC On most other computers you have to key in each letter of, for example, the instruction PRINT. This is inefficient. The ZX81 is very powerful in this respect. The keyboard contains most of the characters in the ZX81 character set and a few special keys. Some 202 different characters are available. Some print on the screen, others are non-printing, e.g. RUBOUT (DELETE). Each of the different types of character 1s described in Section B4. The ZX81 keyboard layout is reproduced in the diagram on the next page. B3: Cursors is] [>] Cursors indicate what operational mode the computer is in and what symbol or name should be typed in next. They appear in inverse video (a white letter in a black square). Keyword mode. ZX81 expects a command a line number or a keyword Keywords are the symbols printed on the keyboard above the keys (see keyboard). SHIFTed keys also function in this mode. Letter mode. Occurs at most other times. ZX81 expectsa letter a number an operator ora special command SHIFTed keys function in this mode. Function mode. Obtained by pressing FUNCTION key (SHIFT, NEWLINE/ENTER). The functions obtainable are printed under each key in white. 10 Figure 2 ZX81 KEYBOARD ГЫ 86791 s e Se a e M CODE PEEK IT ap ж JE es DS Mei ш ч" AG БЕЙ K [ENTER] ARCSIN = Ж: DS COPY CLEAR fis Only one function can be obtained each time FUNCTION is pressed. Graphics mode. Obtained by pressing GRAPHICS key (SHIFT, 9). Mode lasts until the GRAPHICS key is pressed again. In the graphics mode 36 different characters are obtained by pressing the keys with the SHIFT key depressed as well. These are shifted graphics characters. 38 different characters (mainly letters printed in the inverse mode) are obtained by pressing the keys. [s | Syntax error cursor. This cursor appears in a statement line at the bottom of the screen if the computer finds that there is an error in it. It appears when we try to enter an incorrect line of program into memory (i.e. after we press NEWLINE (ENTER) when at the bottom of the screen). The [S | cursor appears next to the last error in the line. (There can be more than one). Editing on the line сап take place immediately. The [5 | cursor disappears when an edit operation is performed. It will re-appear (if necessary) when NEWLINE (ENTER) is pressed again. Current line cursor. When entering statements into the program the last line to be entered is called the current line and is indicated by this symbol placed after the line number. The movement of this cursor up and down the screen, pointing to different lines, is controlled by the { and ^ keys (SHIFT 6 and 7). If EDIT (SHIFT 1) is pressed, the current line is brought down to the bottom of the screen and can be edited. B4: The Different Character Types THE 6 CHARACTER TYPES ON A KEY If we examine a particular key, say [R ] , we can classify the 6 character types, as seen in the diagram below. RUN LETTER <= ec = INVERSE GRAPHICS GRAPHIC INT - KEYWORD On top of the R key is the word RUN. This is a KEYWORD character. All characters printed on the keyboard in this position are KEYWORDS. KEYWORDS will be printed on the screen if the desired key is pressed when the ZX81 is in KEYWORD MODE (1.е. the cursor is on the screen). Exercise If the | К | cursor is at the bottom left-hand side of the screen then enter a keyword. Press the | PRINT | (P) key. Notice that PRINT appears on the screen but the cursor has changed to an cursor and the computer is in the letter mode. This means that it 1s expecting a letter to be keyed in next, e.g. A. If we try to key in another keyword, e.g. , the keyword PLOT does not appear. Instead the letter O is printed. So the rule is: No two keywords may be entered in succession. To clear the screen and return to mode press keys together. Try it. Print different keywords on the screen. Which one does not print? LETTER The LETTER characters (or OWERTY characters as they are sometimes called) are the bold type letters on each key. They are identical to those on a typewriter keyboard. It is worth trying to memorise these. Do it by lines, and in groups of five. Letter characters may be keyed in when the computer is in the letter mode and the cursor appears in the entered program line, or at the bottom left-hand side of the screen. Certain letters may be entered in the mode as default when there is no keyword on that key, e.g. the digits 0-9 and the full stop[ e] [BREAK] is also an exception. A space Is printed in the mode. 13 Exercise Key in | PRINT | to obtain the mode. Then key in the letters, starting from [1]. What happens with | NEWLINE (ENTER)| and |SPACE |? SHIFT There are 39 SHIFT characters on the keyboard. These may be obtained in the Or modes, 1.e. when Or is on the screen. To obtain these characters or symbols e.g. in our diagram, press the | SHIFT | key and the desired | CHARACTER | key at the same time. Exercise Start keying in the SHIFT characters starting with on the top line of the keyboard. Notice what happens with: EDIT THE ARROW KEYS (^4 | e>) GRAPHICS RUBOUT (DELETE) FUNCTION GRAPHICS There are two types of graphics characters, the characters like Bll as in our diagram below, and the letter and shift characters printed in INVERSE (i.e. white letter on black background) on the screen ( Ia). Exercise To print the graphics characters on the screen key in: 14 Keys to Press What happens on the Screen PRINT E] PRINT PRINT ГЕ | PRINT [К | PRINT PRINT [Эй] PRINT NEWLINE (ENTER) ББЗ at top of screen 0/0 at bottom of screen NEWLINE (ENTER) [3 (clears screen) Notice the mode cursor changes. Note that to come out of the mode, you need to press again, to get the cursor back. To clear the screen press | Repeat the exercise and obtain all the graphics characters. Where no graphics character is printed on the key then the inverse of the shift character is obtained by default. ‘Test this out. INVERSE GRAPHICS These characters are the inverse video letter characters, and are obtained in the GRAPHICS mode, i.e. cursor on the screen, when the desired key is pressed. Exercise Key in the characters as before, but this time only press the letters and not the shift characters when in the mode. What happens when you press |SPACE] ? FUNCTION There are 24 Function characters that are obtained only in the Function mode, when the [F ] cursor is on the screen. The ГЕ |cursor is obtained by pressing the |SHIFT | and | FUNCTION | keys together. Only one Function character may be entered. The mode changes to after entry. To input another Function character we need to get back to the mode again. Exercise Get into the FUNCTION mode and key in all the function characters. Key in - Lr] What happens? Press NEWLINE (ENTER) again to clear the screen. HOW TO OBTAIN THE DIFFERENT CHARACTER TYPES Character Number of To Obtain | To Obtain the Type Chars. the Mode: | Character: mmm f 26 | [E] | лонае SHIFT 39 [K ] Automatic SHIFT CHARACTER LETTER 39 Automatic CHARACTER K] (sometimes) mt = = GRAPHICS CHARACTER INVERSE GRAPHICS Е GRAPHICS CHARACTER SHIFT FUNCTION CHARACTER Exercise Using the above table, obtain all the modes and key in example character types. ALPHABETIC CHARACTER/KEY TABLE The following table locates the letter or number key which provides each character (keyword, function, or symbol) on the keyboard. Use this table when entering programs until you are familiar with the placing of all the commands. An * indicates a non-printing character. BASIC Word Keyword (K), Function or Shift and Key to Press ABS Function G LPRINT Shift S ACS Function S NEW (K) A AND Shift 2 NEXT Shift N ASN Function A NOT Function N AT Function C OR Shift W ATN Function D PAUSE Shift M CHR$ Function U PEEK Function O CLEAR (K) X PI (m) Function M CLS (K) V PLOT Function О CODE Function I POKE Function O CONT (K) C PRINT Function P COPY (K) Z RAND Function T COS Function W REM Function E DELETE Shift Ø * RETURN Function Y DIM (K) D RND Function T EDIT Shift 1 * RUBOUT Shift @ * EXP Function X RUN Shift R FAST Shift F SAVE Shift S FOR (K) F SCROLL Shift B FUNCTION Shift NEWLINE(ENTER) SGN Function F GOSUB (K) H SIN Function Q GOTO (K) G SLOW Shift D GRAPHICS Shift 9 * SOR Function H IF (K) U STEP Shift E INKEY$ Function B STOP Shift A INPUT (K) I STR$ Function Y INT Function F TAB Function P LEN Function K TAN Function E LET (K) L THEN Shift 2 LIST (K) K TO Shift 4 LLIST Shift G UNPLOT Function W LN Function Z USR Function L LOAD (K) J VAL Function J 17 SYMBOLS Symbol Cursor and Key Symbol Meaning K or L, Full stop or dec- imal point (Separate key) š K or L, shifted Full stop. Comma ; K or L, shifted X. Semicolon z К or L, shifted 2. Colon ? К or L, shifted C. Question mark `y K or L, shifted P. String quote iis K or L, shifted О. Quote image ( K or L, shifted I. Open bracket ) K or L, shifted O. Close bracket £ K or L, shifted SPACE. Pound $ K or L, shifted U. Dollar + K or L, shifted K. Plus - K or L, shifted J. Minus 7 K ог L, shifted В. Times / K or L, shifted V. Divide те K or L, shifted Н. To power = K or L, shifted L. Equals > K or L, shifted M. Greater than < K or L, shifted N. Less than © = К or L, shifted К. Less than or equal to > = K or L, shifted Y. Greater than or equal to <> K or L, shifted T. Not equal to “= K or L, shifted 5. Cursor left { К ог L, shifted 6. Cursor down T K or L, shifted 7. Cursor up Т” K or L, shifted 8. Cursor right 18 SECTION C: BASIC BASIC C1: The BASIC Language This book is all about BASIC, which is the world's most commonly used computer language. Just as English is a natural language used to communicate with people, BASIC is a formal language used to communicate with COMPUTERS. Like natural languages BASIC has grammatical rules which, although they are fairly simple, must be strictly followed to ensure that the computer understands exactly what it is being instructed to do. BASIC stands for Beginners All-Purpose Symbolic Instruction Code. It was invented in 1964 in the USA and is a combination of simple English and algebra. BASIC is the language we will use throughout this book to write PROGRAMS. Programs instruct the computer what to do, and the sequence in which particular operations are to be performed. BASIC is a high-level programming language. The instructions we write in BASIC are interpreted by a built-in program into the low-level programming language (the MACHINE CODE) that directly controls the switching of the electrical impulses inside the MICROCHIPS which store and manipulate the data. High-level languages like BASIC are far easier to write programs in than the low-level languages, and the simple language and structure of BASIC was designed to be easy to learn. The Sinclair version of BASIC also has single-keystroke entry of BASIC words, which makes mistakes in spelling impossible. C2: A Simple Program A sequence of BASIC statements is called a PROGRAM. Here is an example of a program: 10 INPUT A 20 INPUT B 30 LETS=A+B 40 PRINT S The simple program above adds two numbers keyed in on the keyboard and prints the results on the screen. A program is keyed (or typed or input or entered) into the computer by you, the programmer, line by line, from the keyboard. Before we key a program in we design it to make the computer do exactly what we want. We first write a program down line by line on a piece of paper. This is called CODING. After coding the program we key it into the computer and RUN it. To RUN it we give the computer a COMMAND to RUN the program to see if it works. It probably won't work the first time, unless it's as 19 simple as our example. A program which doesn’t work as intended is said to contain ERRORS or BUGS. If we have asked it to do something it can’t do, or forgotten to include an instruction the computer will tell us what is wrong and give us an ERROR MESSAGE. If the program runs without error messages but doesn’t do what we wanted it to then it is the programmers’ fault. In either case we need to correct or EDIT or DEBUG the program. We do this whilst the program is in the computer, using the editing facilities of the computer. Editing or revising a program is called PROGRAM DEVELOPMENT. When the editing is finished and the program works we take a LISTING of the program on the PRINTER. We can also SAVE a copy of our program on cassette tape and STORE it so that we can LOAD it back into the computer. The complete exercise of designing, coding, developing and documenting a program is called PROGRAMMING. C3: A Statement This is a BASIC statement: 10 INPUT A A statement is also called a LINE. A statement can: (1) instruct the computer to do something (2) state something A statement is composed of: a line number, e.g. 10 an instruction, e.g. INPUT some variables, e.g. A Statements are either: Executable — those which specify a program action, as with our INPUT A, or Non-Executable — those which provide information for the user of the program. All variables (e.g. A in our example) must be initialised to a start value before being used in a program. In this case the statement: 10 INPUTA tells the computer to request the user to input a value for the variable A from the keyboard. C4: Statement Numbers Each BASIC statement or line must begin with a statement number, as with 20 in this example. 20 INPUT B The number 20 is called a statement number or line number. The statement number is chosen by you, the programmer. It may be any number from 1 to 9999 inclusive. ‘The computer uses the numbers to keep the statements in order. Each statement has a unique statement 20 number. If you use the same statement number twice, the second line will replace the first. Statements may be keyed in via the keyboard in any order. The computer sorts them into the correct sequence. Statements are usually numbered in tens so that additional statements are easily inserted later. For example: 10 INPUT А 20 INPUT B 25 INPUT C (Inserted line) 30 LET S=A+B The computer runs the program in order of statement numbers. C5: Instructions A statement gives an instruction to the computer. In this example it is LET. 30 LETS=A+B Instructions are called statement types because they identify a type of statement. In our example the statement is a LET statement. It tells the computer to let the variable S have a value equal to the sum of the values of variable A and variable B. C6: Numeric Variables A numeric variable is the name given to a storage location which holds a number in the computer's memory. A numeric variable can have a name which is: A letter from A-Z or A letter followed by a number or A group of letters and numbers Variable names must start with a letter. Examples of numeric variables: A NUMBER 1 Numeric variables are used to represent numbers inside the computer. We can give (or assign) different values to a variable. The numbers we give to variables are used in calculations. Variables are symbols or names given to parameters or quantities. They represent the VALUE of the parameter, i.e. the number stored 21 in the named memory location. We can use variable names which remind us of the parameter concerned, but they should not be too long or you will find them tiresome to key in (which is why single letters are usually used). For example, we could use: S — Speed PRICE - Price of fish SUM 1 - Sum of the first set of numbers R3 - Resistor Three In our program the statement 10 INPUT A sets up a variable in the computer's memory with the symbolic name A. We could have called it NUM1, or even FIRSTNUMBER. The statement tells the computer to ask us to input a value for À when we run the program. If we key in the number 3 the memory cell allocated to A will contain the number 3. This value is then used in all calculations involving À until we change its value. In the statement: 30 LETS=A+B S, A and B are the variables in the algebraic equation S= A + B. Š is our ‘unknown’ and will take the sum of the values of A and B. The computer will work out the value of A + B and put the result in the memory cell it has allocated to the variable S. The computer will not let us input LET A+ B = S (it will give us a syntax error), because the variable to be given a value must come first. A + B is not a valid variable name. Variables are so-called because their values can vary or change, according to the values we input, or in the course of a program, when we instruct the computer to do something which causes the value to change. For CONSTANTS, which are quantities which do not change their value, we set up a variable in the same way, by giving it a name and a value with a LET statement and let it keep the same value — a variable that doesn't vary! Variable names may be of any length, but they must start with a letter, and must only contain the alphanumeric characters (the letters A to Z and the numbers @ to 9). They can have spaces included, but this is unwise, as it is easy to key іп PRICEI, for example, when you initialised a variable as PRICE 1. The computer will consider them to be two different variables. The inverse video (white on black) characters also cannot be used in variable names. 22 C7: Strings and String Variables STRING A STRING is a group of characters enclosed by quotation marks. The following are examples of strings: “PETER” “12345” “JANUARY 1ST, 1982” sot “Жы А, “REF:A2” As well as numbers, computers can also handle text or groups of characters. Го define a group of characters as a string, we have to place quotation marks at the beginning and end. This tells the computer, for example, that the string ‘“TOTAL’’ means the characters T,O,T,A,L, and not the numeric variable TOTAL, which is a number. Strings can contain any character which prints on the screen, plus spaces, but a string cannot contain quotation marks, because the computer thinks it has got to the end of the string when it gets to the second quotation mark. Now that you know what a string is, we can tell you that strings can be handled by string variables, just as numbers can be manipulated with numeric variables. STRING VARIABLE A string variable is used to store strings. It consists of a single letter (A to Z) followed by the $ sign. For example: A$, Z$, M$ We allocate (or assign) strings to string variables with LET statements, as with numeric variables. For example: 10 LET A$=‘‘STRING 1" 20 PRINT A$ The memory store allocated to A$ will contain the string ‘STRING 1’ (line 10). When we RUN the program the computer will print the contents of memory store A$ on the screen (line 20), i.e. STRING 1. Note the string is printed without the quotation marks. The string is just the characters inside the quotes. 22 C8: Operators and Operands OPERATORS Operators perform arithmetic, logical or conditional operations on variables or numbers. In our program the line: 39 LETS=A+B uses the two arithmetic operators = and + OPERANDS Operands are the variables or numbers which are manipulated (i.e. operated on) by the operators. In the line: 30 LET S=A+B the variables S, A and B are operands. C9: Format of Statements BASIC is a ‘free format’ language. The computer will ignore extra blank spaces in a statement. The following statements are equivalent: 10 INPUT A 10 INPUT A 10 INPUT A The computer will automatically leave spaces after each line number and a space after keywords. It will list programs with all the other spaces you include between instructions and variables. It will ignore them when you run the program. C10: Keying in a Statement Statement to be keyed in: 10 INPUTA Press If your computer system is set up and ready for use (see Section B1) the cursor will be in the bottom left-hand corner of the screen. You can now key in the first statement. 24 Character or Cursor Keys to What appears instruction Press on the Screen to key in [к] 2 2 19 [к] ж INPUT I 19 INPUT A [z]. A i mera [Z] * NEWLINE (ENTER) Entered line is transferred to top of screen * on Spectrum in CAPS mode PRESS NEWLINE (ENTER) AFTER EACH STATEMENT The |NEWLINE (ENTER)| key must be pressed after each statement has been entered. 10 INPUT A 20 INPUT В 30 LET S =A+B[NEWLINE (ENTER) | 40 PRINTS Pressing the | NEWLINE (ENTER) | key informs the computer that the statement is complete. The computer checks the line for mistakes then transfers the statement to the top of the screen and returns the cursor to the left-hand side of the screen, ready for us to enter the next program line. Notice that the line at the top of the screen now contains the CURRENT LINE CURSOR: This indicates the last program line entered and accepted by the computer. It appears immediately after the line number: 10 [>] INPUT A 25 C11: Correcting Errors RUBOUT (DELETE) The RUBOUT (DELETE) key acts as a backspace, deleting the character symbol or keyword immediately preceding (to the left of) it. As we type in a line we may press the wrong key. For example, we might get: 10 INPUTS where we pressed S instead of A. To correct this we press RUBOUT (DELETE) and we get: 10 INPUT We may now continue and type in A. The horizontal arrow keys move the cursor one character or keyword to the left or right along a line as indicated. For obvious reasons, these keys are also referred to as cursor control keys. To correct an earlier mistake on a line (a) Use the arrow keys to move the cursor to a position immediately to the right of the character to be changed. (b) Press RUBOUT (DELETE) to delete the incorrect character, and key in the correct character. (c) Use the arrow key to return the cursor to the end of the line, if you have more to key in. Otherwise, you may press NEWLINE (ENTER) immediately. It does not matter if the cursor is In the middle of the line. To delete a complete line This can be done by using the > key to get the cursor to the end of the line, if you are not there already, and then using RUBOUT DELETE) repeatedly until the line is completely deleted and just the cursor remains. This is tedious on a ZX81, without the Spectrum’s repeat key, especially on a long line. A better way is: (1) Press EDIT (2) Press NEWLINE (ENTER) 26 If you are keying in the first line of a program and there are no existing lines at the top of the screen, pressing EDIT will clear the line. If there are program lines at the top of the screen, pressing EDIT clears we current line and brings down the program line marked with the cursor. Pressing NEWLINE (ENTER) sends this line up again г. clears (һе current line. Exercises 1 Start keying in the first line of the program. Don’t press NEWLINE (ENTER). Play around with the cursor control keys and RUBOUT (DELETE). Delete the complete line. 3 Key in the first line and press NEWLINE (ENTER). Key in the second line. 4 Delete the second line using EDIT and NEWLINE (ENTER). 5 Кеуіп the second line. Key in the third line to read: 30 LET X =A + B. Press NEWLINE (ENTER) Use EDIT to bring this line down again. Use the cursor control keys to put the cursor to the right of X and delete it. Insert S. Leave the cursor where it is, and press NEWLINE (ENTER) to send the line to the top of the screen. 6 Key in the complete program. N C12: Commands COMMANDS are direct instructions to the computer. They are executed immediately. They do not need line numbers, as they are not part of a program. Commands give us direct control over the computer. Examples are: RUN LIST BREAK SAVE To execute a command, we key it in. If it is a command that is printed, it will appear on the bottom line of the screen. This area of the screen must be empty. Then press [NEWLINE (ENTER). Some commands are executed instantly, without pressing NEWLINE ie i (e.g. BREAK), and are not printed on the screen. Most commands are also used as instructions in programs. Some of the commands that can be used as direct commands are not actually very useful in this role. Equally, some that could be used in programs never are. However, each command has a key role to play in the 27 BASIC language and we will deal with the individual commands as we encounter them in the text. You have already met the NEWLINE (ENTER), RUBOUT (DELETE), < and -” commands, and the mode commands (GRAPHICS and FUNCTION). Together with EDIT, RUBOUT (DELETE) and BREAK, plus the f and $ arrow keys, these are the commands that don’t print, and act instantly. All the others need NEWLINE (ENTER) to be activated. C13: Editing the Program EDIT The EDIT command copies the program line indicated by the cursor at the top of the screen, to the bottom of the screen, replacing any current line. The line brought down can then be edited or changed. EDIT may also be used for entering lines that are similar where only the line number changes: (1) Key in the line. (2) Press NEWLINE (ENTER) - line goes to top of screen. (3) Press EDIT - line copied to bottom of screen. (4) Use RUBOUT (DELETE) to delete the line number. (5) Key in new line number. (6) Press NEWLINE (ENTER) - new line goes to top of screen. The same procedure can also be useful with lines which only vary slightly, i.e. perhaps only the line number and a variable are different. If you can save keystrokes by bringing down a line and revising it, then do so. The technique is as above, but after (5) you must use the cursor control keys to shift the L-cursor along the line and use RUBOUT (DELETE) to erase the variable (or keyword) that needs to be changed. Insert the new character, and press NEWLINE (ENTER). These commands move the cursor in the entered program at the top of the screen from one line to another. This enables us to then copy down any line in the program for editing using [EDIT]. Deleting a line in the entered program To delete a given program line which has been entered and is at the top 28 of the screen just type the line number and press NEWLINE (ENTER). For example: 10 |NEWLINE (ENTER will delete line 10 in the program. You will see it disappear from the screen. C14: Listing a Program on the Screen LIST The program has been entered into memory. To produce a listing on the screen of all lines accepted by the computer key in: LIST NEWLINE (ENTER LIST is a command that prints on the screen. It appears on the bottom of the screen, and is executed when NEWLINE (ENTER) is pressed. LIST N Will list a program starting from program line N. For example, if we key in: LIST 30 NEWLINE (ENTER our program will be listed from line 30. We key in LIST, then the line number we want the listing to start at. If we have a program that is longer than will fit on the screen, we use the LIST (line number) command to display successive screenfuls of the program. If the bottom line on the first screen is 210, for example, we would use LIST 220 to get the next set of program lines. Listing a program on the Spectrum which is larger than a screenful produces a SCROLL? prompt. Answering this with anything other than ‘N’ or BREAK scrolls the listing up so that the next screenful of statements can be seen. C15: Running the Program Our simple program has been keyed into the computer line by line and entered into memory. Let's see if it works. We give the computer the command RUN. 29 RUN NEWLINE (ENTER The RUN command starts execution of a program at the lowest numbered statement. Run is a command and is keyed in. It appears at the bottom of the screen. It will not be executed until [NEWLINE (ENTER)] is pressed. When we do this the program starts operating. The screen will go blank and the L-cursor will appear at the bottom. (This will be a C-cursor if you are using a Spectrum in CAPS (capital letter) mode, using CAPS LOCK as we advised.) The computer is now running the program and asking us to input a number for the variable A. Key in the number and press [NEWLINE (ENTER)] . The L-cursor appears again at the bottom of the screen. The computer requests another number, to be assigned to the variable B. Key in the number | 5 | and press . Our result (the number 8) is printed at the top left of the screen. Notice the message that appears on the bottom of the screen. We can also run the program from a line other than the first program line: RUN N RUN (Line Number) This command starts execution of the program from the specified statement (line) number. RUN 20 will start a program at line 20. Note that when the RUN N command is used all statements before the specified statement number (N) will be ignored and any variables defined in these statements will be considered by the computer to be undefined because it has not RUN the lines. The program will not work and an error message will result. All values of variables are wiped out by the RUN command. We can RUN the program as many times as we wish: Key in [| NEWLINE (ENTER) | again If the program has been run once and the message is at the bottom of the screen, to rerun the program key in RUN. This overwrites the message and pressing NEWLINE (ENTER) starts the computer operating the program. The L-cursor appears to prompt for an input again (C-cursor for Spectrum in CAPS mode). 30 The screen is now blank. We can get the program listing back very easily: Press NEWLINE (ENTER) After running the program, the program listing re-appears at the top of the screen if the NEWLINE (ENTER) key is pressed. The program can now be edited if necessary. C16: Error Messages Our computer tells us it has finished running the program by giving us a message. On the ZX81 this will be: 0/40 at the bottom of the screen. The Spectrum gives an expanded version of the message: 0 OK, 40:1 This tells us that no errors were found and the program finished at line 40 (the last line). The number after the colon can be ignored in most Spectrum error messages, as it refers to multiple-statement lines. We shall not use these in this text. There is one case where it is 2, as we shall see later. These special diagnostic messages appear at the bottom of the screen every time a program is run. If the program does not work a message appears with the form: E/N E is a number or a letter indicating the type of error that has caused the program to stop, and N the line number where the program halted due to the error. The Spectrum adds a message briefly stating the cause of the error. We look up the meaning of E in the list of Error Codes in Appendix II. This helps us to correct or debug the program, since we know what sort of problem has occurred and which program line it happened at. Exercises 1 Run the program on page 19 a number of times keying in different values for A and B. 2 Press NEWLINE (ENTER) to get the listing. Change line 30 to read: 30 LETS-A-«C 31 Now RUN the program. The error message 2/30 (on the ZX81) appears. On the Spectrum we get 2: Variable not found 30;1. So we have a type 2 error and the program stopped at line 30. A type 2 error means we have forgotten to define a variable. We are now using the variable C instead of B, but we have not yet given C a value, and the computer could not complete the operation of line 30 due to insufficient information. Insert a new line: 25 INPUT C and run the program again. It now works. Why did the program originally stop at line 30? Why do we now have to key in 3 numbers to make it work? 3 Add an extra line at the beginning of the program. Key in: 5 PRINT “PROGRAM ADDS 2 NUMBERS" RUN the program, starting from different lines by using: RUN RUN 10 RUN 15 Why do you think RUN 15 does not work? 4 Edit the program to obtain the original version. C17: How the Program Works Line 10 tells the computer that a number must be input and given the name A, (i.e. assigned to the variable A). ‘The computer reads the line and prints an at the bottom of the screen,* reminding us to input a number. The computer will wait until we key in a number. The number is then stored in memory cell A. The computer goes to the next line. Line 20 tells the computer that another number, to be assigned to the variable B, must be input. appears at the bottom of the screen* and the computer waits until we key in a second number, which is stored in memory cell B. The computer goes to the next line. Line 30 tells the computer that a variable 5 18 to be assigned the value of the sum of the variables A and B. The numbers in cells A and B are added 10 INPUT A 20 INPUT B 30 LETS=A+B *This will be a C-cursor if using a Spectrum with the CAPS LOCK facility used, as Spectrum users must do throughout this text to get program listings which appear the same as the ones in the text. Use the CAPS SHIFT and CAPS LOCK keys simultaneously on switch-on, and remember that the C-cursor will appear instead of the L-cursor. We will not mention this again. 32 and placed in cell S. The computer goes to the next line. Line 40 instructs the computer to output the 40 PRINT S value of Š to the screen. The computer looks for the next line. The computer can find no more statements to execute in the program and gives a message 0/40 on the screen telling us that the program finished with zero errors at line 40. The Spectrum gives the same message, in the form 0 OK, 40:1. The computer now waits for more commands. C18: Naming the Program 5 REM “NAME” Programs are named in a REM statement. The program name is enclosed in quotation marks. The program is usually named in the first statement in the program. We need to give our program a name in order to: (1) Differentiate it from other programs (2) Store it permanently on cassette tape (SAVE it) (3) Put it back into the computer from cassette tape in order to run it (LOAD it). The program name can be any combination of characters and any length on the ZX81. On the Spectrum, program names for use with the SAVE and LOAD instructions must start with a letter, and can only have 10 characters in the name. It is sensible to keep the program name short and relevant to the type of program, although some programmers name programs after themselves: “PETER 1” “PETER 2" ete. Programs which undertake various kinds of statistical analysis could be named: "STATS “STATS2” etc, Programs which perform calculations for experiments in the laboratory could be named: "OPTICS З” “FRICTION” “TITRATION” etc. If spaces are used in program names, it is easy to misread them, or forget that there should be a space. If the program name is not one word, we can use an asterisk: “FETTER?” “FOCALLENGTH” etc. ((FOCAL*LEN"' for the Spectrum) 33 Program names and cassette tape codes should be recorded in a DIRECTORY which enables us to access a PROGRAM LIBRARY of programs stored on tape. We need to name our program: List the program and add a line which names the program. For example: 5 КЕМ “SUMPROG” or S REM “PROGI” could be used. We will call our program “АПОПОЕК”, so key in 5 REM “ADDER” 34 SECTION D: SAVING, LOADING AND LISTING D1: Saving the Program on Cassette Tape We need to save programs on to cassette tape (the off-line storage medium the Sinclair computers use) because when the power supply is switched off (or disrupted - variations in the mains supply can affect the computer) the RAM memory and the registers in the CPU are cleared and we lose the program. The memory is said to be volatile. This means we have to key it in again — not too bad for a 5 line program, but a 50 liner will take you an hour! If we had made a copy of the program on to magnetic cassette tape using the SAVE command we could have reloaded it into the computer quickly, using the LOAD command. Tape storage is not the quickest or most reliable method used for off-line storage, but it works, and has the advantage of low cost. The ZX81 reads and writes tape fairly slowly in computer terms, and a large program will take some minutes to LOAD or SAVE. The Spectrum loads programs several times faster. Software (programs) stored on tape is available for use when needed, making it PERMANENT. Software also has to be PORTABLE. Programs we write can be used by other people with the same computer, or software available on cassette can be bought. SAVE SAVE “NAME” The SAVE command outputs the program and variables to the cassette recorder. If the cassette recorder is in record mode then a copy of the program will be made on the tape. Spectrum users please note that the program name for SAVEing must be 10 letters or less. The name can be in either upper or lower case (or a mixture) but exactly the same name must be used to LOAD. It is safer to choose to use capitals only. SAVING THE PROGRAM 1 Check that the cassette recorder is plugged in (or has good batteries). 2 Ensure it is connected to the computer, with the MIC- MIC sockets being connected. See the important Spectrum note below. 35 мы GO Set the TONE control on the cassette recorder to HIGH. Set the volume control on the cassette recorder to 3/4 of MAXIMUM. Insert a new C12 computer cassette tape into the recorder. Short cassettes are more convenient than long ones for our purposes. Run the tape through on FAST FORWARD and then REWIND to ensure equal tension. Set the tape counter to zero and run the tape forward five revolutions (about 20 or 30 seconds). List the program on the screen and printer. Check the program is named (e.g. ‘‘ADDER’’) іп a REM statement. ZX81 Sequence 10 11 12 13 14 15 Type SAVE “ADDER” don't press NEWLINE (ENTER) yet. Press RECORD and PLAY buttons on the recorder. Press [NEWLINE (ENTER) ]. Watch the screen. a) For five seconds it will be grey inversed by diagonal white lines and if the sound on the TV is turned up it will be a monotone. This is the SILENT LEAD IN b) For ten seconds a horizontal striped pattern appears on the screen. This is the program going in. A warbling sound is first heard, then half second pulses. с) Тһе screen goes white and the message 0/0 appears, telling us the computer has transmitted the program to the cassette recorder. The ZX81 does not know whether the recording is successful. We can only tell by later loading the program back in. Stop the recorder Note the counter reading at the end of the program. Run the tape forward five more revolutions of the counter, ready for the next program. Spectrum Sequence IMPORTANT NOTE: YOU MUST ALWAYS TAKE THE JACK-PLUG OUT OF THE EAR SOCKET OF THE SPECTRUM BEFORE ATTEMPTING TO SAVE A PROGRAM. 36 10 Key in SAVE “ADDER”. 11 Press ENTER. The Spectrum will print a message on the screen which tells you to ‘Start tape’, i.e. press RECORD (or record and play, depending on your cassette recorder), and “then press any key'. Do so. 12 Blue and red lines (black and grey оп a black and white TV) will scroll up the border area of your TV screen. This happens twice as the name of the program is recorded. When the program is copied, narrow yellow and blue/black lines roll up the border area. When the recording is complete an *0 OK" report appears on the screen. Stop the recorder. Note the tape counter reading. Your program should now be correctly recorded. 13 On the Spectrum, you can check this without wiping out the program in memory first. Connect the EAR lead from the Spectrum to the cassette player EAR socket. Rewind the cassette to before the start of your recorded program. Get into the E mode, and key in VERIFY, then enter the program name between quotes. Press ENTER and start the cassette on PLAY. The Spectrum displays on the screen any other programs before the specified one that it finds on the tape, printing their names on the screen. 14 When the program has finished playing back, an “0 OK’ message means the program was correctly SAVEd, and *R Tape loading error' means the recording is faulty and you should SAVE the program again. 15 Run the cassette on five more revolutions of the tape counter, ready for the next program. The sequence above assumes a tape counter on your cassette recorder. Without a counter, the process of finding a program is more difficult. To place a voice message on the tape, so that the tape is searched for the voice giving the program name, will prevent the tape being searched automatically by the computer, but it 1s one possible method. If used, you should record your voice (most cassette machines have a built-in microphone) stating the program name several times, then the program name should be spelt out, the name stated again, and some cue statement (“saving starts now’) to let you know that after that point only computer-generated noises exist. This will make finding the program much easier, as the voice cues occupy a larger length of tape than a single statement of program name. The other alternatives are to place only one program on each tape (a bit uneconomical!) or to leave very large gaps between tapes (30 seconds at least), so that you can search using fast forward/reverse and are unlikely to miss the gap. This has the advantage that you can set the computer to search through the tape program by program if you do miss it. Larger programs should be placed if possible on a side of a 37 cassette by themselves. Short length cassettes are available (5 minutes a side) to make this a viable option. Exercises 1 Try a dummy run first. Do not press the recorder keys. Turn up the sound on the ТУ until you can hear a hum. Awful, isn’t it! Key in SAVE “ADDER?” and press NEWLINE (ENTER). (Press a key in response to the message if using a Spectrum). Watch the screen and listen to the different sounds. When the screen clears and the 0/0 message appears (0 ОК, 0:1 оп а Spectrum), key in LIST NEWLINE (ENTER) to get the listing back. 2 Now SAVE the program on to the tape. D2: Deleting the Program from Memory A sure way is to switch off the power - this is not recommended. This should only be done if the computer needs to be re-set because it will not respond to commands keyed in. It is much better to use the command NEW. NEW The NEW command deletes any current program and variables from the computer and clears the screen. We use the NEW command before we LOAD a program into the computer from cassette tape, to erase old programs and data from memory. It is also used to do the same thing, if we have a program in the computer and wish to clear it out to enter another. There is another command that only affects the variables store, and not both this store and the program store, as NEW does. CLEAR The CLEAR command erases all the variables in the current memory. CLEAR can be used as an instruction in a program, as can NEW, but since NEW would merely wipe the program its use would be self- defeating. Try it, if you like the idea of a program that self-destructs! 38 CLEAR is similarly useless in the middle of a program - we would merely have to re-define all variables. With our program, if we RUN it, at the end of the run it will have in the variables store the values of A, B and S. If we then SAVE it, these values are SAV Ed also. In our case this is irrelevant, since the INPUTSs will change them when it is used but often it is useful. We can store data as variables in a program, and not have to re-input values (as long as certain procedures are followed, as we will see later). This enables us to have, for example, a telephone directory stored in variables. We might then use CLEAR to wipe one list, and re-input new data or use CLEAR before SAV Eing the program to send to a friend for his use. CLEAR acts slightly differently on the Spectrum (see page 458), but for our purposes at this point the difference is insignificant. The major function is the same. It is very easy to key CLEAR by accident on the Spectrum, so be careful! Exercises 1 RUN “ADDER”. Enter NEWLINE (ENTER)| to clear the screen. Enter GOTO 40, then press NEWLINE (ENTER). The computer will print the value of 5. Now enter and then GOTO 40 (NEWLINE/ ENTER) again. We then get an error message 2/40 (2 variable not found, 40:1 on the Spectrum) indicating an undefined variable, because the computer has wiped the value of S. We will deal with GOTO in due course. Just follow the instructions for now. 2 LIST the program ‘‘ADDER”’ on the screen. Press and . The listing will disappear and the cursor appears. On the Spectrum, when NEW is followed by ENTER, the screen will go black for a moment then become white, with the words ‘© 1982 Sinclair Research Ltd’ at the bottom of the screen. 3. Press and then [NEWLINE (ENTER) ]. What happens? Why? 4 Key in the first line of the program and press NEWLINE (ENTER). Switch off the power supply (by pulling out the jack- plug). Switch it on again (by re-inserting the jack-plug). What happens? 5 Re-enter ‘‘ADDER’’. D-3 39 D3: Loading the Program from Cassette Tape LOAD “NAME” The command LOAD “МАМЕ” waits for the cassette to play the portion of tape with the program called “NAME” and copies the program, with its variables into the computer’s memory. This means that we can start the tape, give the command LOAD “МАМЕ”, and the computer loads nothing into its memory until the signal it recognises as NAME appears on tape. We can thus search a tape for a program. The Spectrum will print on the screen the names of any programs it finds on tape, before it encounters the specified program. LOAD “” The LOAD “” (nothing between the quotes) command LOADS the first program it finds on the tape. N LOADING PROCEDURE ON THE 4Х81 Place the tape with the desired program in the cassette player. Position the tape via the counter to just before the location of the required program. Clear the computer’s memory using the command if there’s a program in memory. Set the TONE control on the tape recorder to nearly Maximum (High), and the VOLUME control to % Maximum. Key in LOAD “ADDER” or the appropriate name. Don’t press NEWLINE (ENTER). Depress the PLAY key on the cassette recorder. Press NEWLINE (ENTER). A thin diagonal pattern will appear on the screen with a single tone sound. The pattern changes to broad horizontal stripes with thinner diagonal stripes and half second sound pulses are heard as the program is loaded in. The screen clears and а 0/0 message indicates the loading is a success. STOP the recorder. 40 10 11 COND л 10 11 12 LIST and RUN the program. Remove the tape when finished. LOADING PROCEDURE ON THE SPECTRUM Place the tape with the desired program in the cassette player. Position the tape via the counter to just before the location of the required program. Clear the computer’s memory using the NEW command if there’s a program in memory. Set the TONE control on the tape recorder to nearly MAX (High), and the VOLUME control to % MAX. Key in LOAD ‘‘ADDER’’, but don’t press ENTER yet. Press the PLAY button on your cassette recorder. Press ENTER. When the Spectrum has found a program it will scroll blue and red bands of colour up the border area. The name of the program will be printed to the screen and then the blue and red lines repeated again. If the correct program has been located, then it will LOAD with a finer set of blue and yellow lines scrolling up the border area. If not, the border area will flash blue and red alternately as it carries on to the next program on the tape. When the program is correctly loaded, the phrase: 0 OK, 0:1 will appear at the bottom of the screen to indicate that all is well. Stop the recorder. LIST and RUN the program. Remove the tape when finished. CAUSES OF FAILURE TO LOAD 1 3 Volume too low. Volume too high. Tone too low. These indicate that the program has been played at the wrong settings. New volume and tone adjustments will have to be made. Some indications of these problems are visible on the screen display of the ZX81, although systems vary in their response. Appendix IV has a procedure for adjusting tone and volume settings for the ZX81, as well as some general hints on tape use. Experiment and get to know the patterns produced during LOAD on your ZX81. 41 4 Loading started in the middle of the program. If a mistake has been made with the start position, rewind the tape completely and let the computer search for the program name. 5 The program is not on the tape. Check your directory, and the writing on the cassette. 6 Тһе program name is incorrect. Try again, making sure you have spelt it correctly in the LOAD instruction. If you fail again, run through the tape using the LOAD ““””' command. This will load the first program each time. Stop the cassette player after each load and LIST the program to check. (This is not necessary on the Spectrum.) If it's not the program you want, repeat for the next program on the tape. The Spectrum will print the name of all programs оп tape if you use a LOAD “ZZZ” instruction, i.e. a name that does not exist as a program name. 7 Pick up from stray electromagnetic fields. This will show as violent interference on the screen, distorting the patterns together with excessive hum on the sound. It could originate from the ГУ itself, feedback between the recorder and the computer or an external field. Switch off any radio that is in the vicinity. Take out the jack-plug from the MIC socket of the cassette player, as this will break the feedback loop that can exist between the computer and the cassette player. The Spectrum has fewer LOADing problems than the ZX81. It will accept a much greater variation in both the volume and tone of the signal. However, it is worth noting that if there are great differences between the recorder the tape was recorded on and the one it is played back on (variations in tape-head azimuth is often the main source of the problem), then LOADing can be almost impossible, even on the Spectrum. As we noted at the beginning of the book, the Spectrum, unlike the ZX81, offers a choice of upper and lower case letters. Ensure that if you have used lower case ones in the program's name, then you use them again in the LOAD “ххх” command. The same applies if you use upper case letters to name a program. Thus, a program named “MATHS” will not LOAD with the statement: LOAD ‘‘maths’’. Some further information concerning the use of cassette tapes, and advice for the ZX81 if problems are encountered is given in Appendix IV. Exercises 1 Load the program “ADDER”. LIST and RUN it. Delete it from memory, using NEW. Try loading it with different volume and tone setting. Estimate the volume and tone ranges for which it will not load. If you have a ZX81, you can do this by watching how the screen 42 patterns change when you change the settings while the program is loading. Read Appendix IV. D4: Listing the Program on the Printer LLIST LLIST lists the program currently in the computer memory on the printer, starting from the first program line. LLIST N LLIST N lists the program on the printer starting from line N. We can stop the listing by pressing (BREAK needs CAPS SHIFT on the Spectrum). This stops the listing with an error message D/line number on the ZX81 and D BREAK - CONT repeats 0:1 on the Spectrum. It is important that you keep a listing or printed record of all the programs you write or use. The listings are a great help in debugging programs (both under development and if there are problems discovered later). We can key the program back in from this listing, if necessary. Printouts also form part of the documentation for a program and should be pasted into a notebook. Printed records of program results can also be kept using the COPY command. Exercises 1 LLIST the program ‘‘ADDER”’ on the printer. 2 ‘Try stopping the listing with the BREAK key. The listing cannot be continued by pressing CONT (try it). On the Spectrum, despite what it says, this doesn't work. The screen just goes blank. Don't worry. Press BREAK again. 3 List the program on the screen. Use the COPY command to list the program on the printer. What is the difference between the two listings obtained with LLIST and COPY? 43 D5: Program Libraries and Directories LIBRARY A collection of programs stored on cassette tape. For example: COMPUTERLAB PROGRAM LIBRARY or Your own program library. Notice that programs can also be stored on magnetic discs and im ROM memories. DIRECTORY The list of program names in the library together with important information about them. Another name for a directory is CATALOG. You should keep, in your notebook, or a special book, a directory of all programs you have entered and saved on tape. This will seem a bit pointless when you only have a dozen or so, but you will appreciate the need to be systematic when you accumulate a large number. PROGRAMS YOU WRITE Each program you write should be Named. Saved on a cassette tape. Listed on the printer. Documented. Catalogued into the Directory of your own program library. Gm wm G3 N = DOCUMENTATION The complete collection of information about the program or file, written on paper. The information should include: 1 What the program does. How it does it. A listing. A flowchart. How to use it. When it was written and by whom. Q3 Gr мы CS N 44 We will introduce flowcharts in Section G. DIRECTORY LAYOUT A typical layout for the Directory Section of your notebook would be: Program Name: MOONLANDER Cassette Name: GAMES 3 Locatton: 100-120 Program Length: 30 lines Date Created: 18.5.82 Author: PAUL NIXON Function: Lands a spaceship on the moon WRITING ON THE CASSETTE There is a label on each side of the cassette. Write on each side: 1) Cassette name or code. 2) Date. 3) Program names as they are copied into it. Make sure these are correctly spelt! Your directory should provide you with the more detailed information, such as precisely where the program is to be found. 45 SECTION F: IMPROVING THE PROGRAM E1: Adding Comments REM The REM statement is used for adding comments to a program. All REM statements are ignored by the computer when the program is RUN. These comment statements are for the users’ benefit only. They contain information in the text of the program which explains what the program is doing. For example: REM **THIS PROGRAM ADDS TWO NUMBERS KEYED IN AND PRINTS THE RESULTS** Notice the use of the asterisks to separate the text from the instruction. 100 REM ** END OF PROGRAM** The complete program including all REM statements appears on the screen or printer when using the LIST and LLIST commands. Our saved program so far looks like this: 5 REM “ADDER” 10 INPUTA 20 INPUT B 30 LET S=A+B 4) PRINTS Let us add some additional REM statements: 6 REM **THIS PROGRAM ADDS TWO NUMBERS KEYED IN AND PRINTS THE RESULT** 60 REM **END OF PROGRAM** Key these extra statements in. LIST the program and RUN the program. Do not worry about the line numbers not being in intervals of 10. We will renumber the program when we have added all the extra lines. E2: Using the Print Statement PRINT In our simple program we will use the PRINT statement: a) To print messages and instructions to the user on the screen: 7 PRINT “INPUT TWO NUMBERS" The message INPUT TWO NUMBERS is a string, and will be printed without the quotes. 46 b) To print the numbers keyed in and the result: 40 PRINT A; ‘‘ + ’’;B;‘* = ?°;5 A and B are the names of the variables to which the numbers keyed in are assigned, and S is the variable that stores the sum of A and B, i.e. the result. Variables do not need quotes to be printed. The semicolons (;) tell the computer that we want close printing, with each print item (character or variable) directly after the last, with no spaces between. The inverted commas (quotes) enclosing the symbols + and = means we want those symbols printed. c) To leave spaces between lines printed on the screen: 8 PRINT The PRINT instruction used on its own prints an empty line on the screen. Note that we have changed line 40 from what it was previously. Our program now looks like this: 5 КЕМ “ADDER” 6 REM **THIS PROGRAM ADDS TWO NUMBERS KEYED IN AND PRINTS THE RESULT** 7 PRINT “INPUT TWO NUMBERS” 8 PRINT 10 INPUT A 20 INPUT B 30 LET S=A+B 40 PRINT А‘ + ‘В; = > 58 60 REM **END OF PROGRAM** Key in the new lines and RUN it. E3: Adding a Loop GOTO N The statement GOTO N transfers program execution to the specified line number, N. For example: 50 GOTO 7 When we insert line 50 into our program we can see that, after printing the result on the screen, line 50 sends the computer back to line 7 to execute the program again from that line, and as soon as the computer reaches line 50 again it is sent back to line 7 once more. We have constructed a LOOP. The program is going to carry on looping forever unless we can pull out of it. 47 Our program now is: 5 REM “ADDER” 6 REM **THIS PROGRAM ADDS TWO NUMBERS KEYED IN AND PRINTS THE RESULT** 7 PRINT “INPUT TWO NUMBERS” 8 PRINT 10 INPUT A 20 INPUT B 30 LETS-A-«B 40 PRINT A;" &'B;"UeCUNS 50 GOTO 7 60 REM **END OF PROGRAM** Key in line 50. RUN the program. When you are tired of inputting numbers, read on. E4: Stopping the Program We need to know how to get out of the input loop between lines 7 and 50. The program will wait for an input of a number at line 10 INPUT A. The cursor will appear on the screen. To pull out or stop the program at this stage key in [STOP | [NEWLINE (ENTER)]. STOP is a command we input directly, like RUN. STOP On the ZX81 the STOP command stops a program with the message: D/line number, and on the Spectrum we get H STOP in INPUT (Line number):1. The line number refers to the program line the computer was executing when it was stopped. Our program will give D/10 as the message (H STOP in INPUT 10:1 on the Spectrum). We can cancel the STOP command and continue the program with the CONT command. CONT The CONT command used after the STOP command will continue the program from the line the program was stopped at. 48 Keyin ICONT | INEWLINE(ENTER)| to continue the program. Note the Spectrum prints CONT in full as CONTINUE. Exercise Run the program “АОПЕК”. STOP the program when the first | L | cursor appears. CONTinue the program, and input a value for A. STOP the program when the second cursor appears. Note that the line number is different in the message that appears on the bottom of the screen. CONTinue the program. E5: Testing for a Condition In a program we can make decisions which will affect what the computer does next. A decision is made on the basis of whether a CONDITION is true or false. CONDITION A condition has the form (X) (condition) (Y) where X and Y are numbers, variables or expressions and the condition is a conditional operator. We shall use only the = (equality) operator for the moment. The following are all conditions: X=Y A = 23 B = 2*3 Conditions are tested and the next action determined by the result of the test with the IF and THEN statements used together. IF - THEN An IF - THEN statement has the form: IF (condition) THEN (instruction) For example: IF А = B THEN PRINT “EQUAL” IF A=@ THEN LET A= 3 The instruction can be any valid instruction. The statement means: IF (the condition is TRUE) THEN (perform as instruction). IF (the condition is FALSE) the computer ignores the instruction after THEN and goes to the next line of the program. 49 In our simple program we can use the IF — THEN statement to insert in the program a conditional test which will stop the loop, without using the direct commands which we used in the last Unit. To STOP the program in the same way as with a direct command we can insert another line: 15 IF A«9 THEN STOP This tells the computer that IF A = 0 (if it is TRUE that A is equal to 0) THEN it should STOP. IF A is any other value (if it is FALSE that A = 0) it ignores the THEN STOP instruction and moves to line 20. Enter this line into the program. RUN the program. Enter different non-zero values for A to see that if A 1s not zero then the program continues as before. Enter .000000001 to see that only if A is exactly zero will the STOP instruction be executed. Input 2 for B, and notice that the result is given as 2. This is due to the fact that calculations are only performed to a certain degree of accuracy. Enter .0000001 for A, and input B as 2. The computer returns 2.0000001 as the value of S- the number is within the limits of accuracy. Now enter 0 for A. The program will stop, just as when we entered STOP as a direct command. Notice, however, that the message at the bottom of the screen is different. We get the message 9/15 on the ZX81 (a STOP statement, 15:2 on the Spectrum).* The message is different because STOP in a program means “f the CONT command is received, proceed with the next program line', since if it continued with the same line it would just STOP again! As a direct command, however, STOP means ‘if the CONT command is received, start with the same program line', so that the computer does not miss out a program line. Now we have some extra control over the program, but it is still not satisfactory. We used IF A - 0 because in this program it is not a value we are interested in seeing added to B (a value used in this way is known as a DUMMY or SENTINEL VALUE - a value just used as a signal to the computer which would not need to be entered in the course of normal inputs). This stops the program and we can continue it, but the program just goes back into the loop. We need a method of proceeding out of the loop to end the program, or continuing with more program lines. We can do this with a STRING CONDITION. The conditional operators can also be used to express relations between strings - either string variables or simple strings. We insert the following lines: 30 PRINT “RUN PROGRAM AGAIN ?(YES/NO)" 55 INPUT A$ 56 IF АЗ - ““ҮЕ58” THEN, GOTO 7 “Оп the Spectrum, the statement after the THEN іп an IF- THEN statement is treated as the second statement in the program line. This is why we get 15:2, meaning line 15, statement 2. This is the only instruction used in the main text of this book (before Unit W2) where the statement number will not be 1 in an error message. 50 When the program gets to line 50 it will print out the message, and then put the cursor at the bottom of the screen. Because it has been told that a string input is to come, the cursor has quotes either side: "[L]". There is no need to type quotes. Whatever characters are typed in will be stored as A$. The string is entered by pressing NEWLINE (ENTER) after keying in the characters. Line 56 tells the computer to check if the characters in A$ are the same as the characters of the string ‘‘YES’’. If they are it goes to line 7. If they are not the program will continue to line 60. Notice that any string other than “YES” will cause the program to continue to line 60. Exercises 1 Delete line 15 in our program, which we no longer need. Insert the new lines 50, 55 and 56. 3 RUN the program. Enter “YES” in response to the string input cursor and see that the program loops back to line 7. 4 Next enter “МО” to see that the program goes to line 60 and gives the message 0/60 (0 OK, 60:1 on the Spectrum). Run the program again. This time enter anything other than ‘ҮЕ’ or “МО”, to see that the program goes by default to line 60 if anything other than ''YES"' is entered. 5 Experiment with the string input. What happens if you press NEWLINE (ENTER) without inputting anything? What happens if you try to key in quotes around the string? 6 LLIST the program on the printer. The development of our program is complete, and we have run it to see that it works. It remains to renumber the lines, and this is easier to do if we have a listing. E6: Final Edit and Saving Our program ‘‘ADDER”’ is complete and works. We need, however, to renumber the lines. The procedure for this is as follows: 1) Using the listing from the printer, renumber the statement lines in tens at the side of the old number. You can also count the number of lines in the program on the screen display, and multiply by ten to get the new highest line number. For our program, this will be 120. 2) a) List the program on the screen. b) Usethe ^4 and | cursor control keys to bring the current line cursor to line 60 (the bottom line of the program). c) Press EDIT and pull line 60 down to the bottom of the screen. d) The new HIGHEST line number is 120. e) Change 60 to 120. 31 g) h) J) Press NEWLINE (ENTER). Line 60 remains, but it 1s duplicated by the new line 120. Delete the old line 60 by entering 60 and pressing NEWLINE (ENTER). Change each line number in this way, going from highest to lowest. Lines that contain other line numbers must have these changed to their new numbers. In our program we must remember to change line 56 to: 90 IF A$=‘‘YES’’ THEN GOTO 30 where 3@ is the new line number corresponding to the old line 7. Rename the program ‘‘ADDER2’’, at the same time as you change the line number of line 5 to 10. This program is different from the original version, and must be given a different name both for our reference, and the SAVE and LOAD operations. Run the program to check that it still works, and that we have all the lines, with any GOTO (line number) statements correctly renumbered. LIST and LLIST the program. SAVE “АОПЕК2”. Write the name of the program on the tape cassette, along with the tape counter readings. Put details of the program in your directory. Stick the listing of the program in the notebook you are using for documentation. 52 SECTION F: A GAME INTERLUDE F1: The Program Library In addition to the many programs and subroutines in the main body of the text, there are additional applications and games programs in the Program Library (Appendix VI). Our main objective is to enable you to write your own programs, and the programs in the text have been used to illustrate the use of techniques. Some are functional (do something significant) and some are just illustrative. You don’t have to key all the programs in the text into the computer, but you must understand them. However, you should key in all the shorter programs since it’s important to see how different types of program operate in practice. Analysing the longer programs is vital, even if you don't key them in. The use of flowcharts (to come in Lesson G) is helpful for this. There are also suggestions for programs you should write, to get practice in writing programs to perform tasks, after units dealing with specific techniques. The programs in the library are examples of applications and games programs, plus a number of subroutines for some of the manipulations commonly required in programs. You can key these in at any time if you want to see how the program works, find the program useful, or want to play the game. Once keyed in you can SAVE them on cassette and LOAD them back in quickly. None of the programs are very long, since it is difficult to analyse long programs, and this is what we want you to do. Keying in a program from a listing doesn’t teach you anything about programming, nor does running it. Writing or modifying a program does! We hope you find the programs entertaining or useful, but please treat them as a source of ideas and illustrations about programming, not as a fixed set of optimum solutions. Programs can always be improved! Be careful when keying in programs, especially if you don't understand how they work. (It might be better to work this out first - because, to labour the point, that way you'll learn something.) The S-cursor will mark some errors in lines for you and stop you entering them, but there are always other problems you can introduce. Check through your listing for errors and missing lines (surprisingly easy to do, even with numbered lines) before you run the program. You must also be careful to check that any necessary alterations have been made to the program if you are going to run it on a Spectrum, as noted in Unit W2. These are mostly minor but can be crucial. F2: A Game to Key In You have now spent a lot of time working through the essentials of your computer system and its BASIC, and you probably have the feeling 53 that thus far you haven't seen anything to persuade you that computers are particularly exciting machines. Far from being impressed by their capabilities, you may well be thinking, ‘What’s so good about a computer if you need to do all this to get it to do something that I could do in my head when I was six?’ Well, the following program may not be earth-shattering, but it does in fact reveal a fairly complex set of computer operations, as well as providing amusement. The program is called **BUG"' and it enables you to play a game that consists of dropping bricks from a height to squash the 'spider' (an asterisk) scurrying along below. If you have a militaristic or SF streak in your nature, or are an arachnid lover, feel free to change the name to “BOMBER” or whatever (in line 5). Whether you will enjoy it more by pretending you're napalming Venusians is your affair. It won't alter how the program works! To play the game, however, you first have to key it in. You won't understand at this point how it works (and won't for a few chapters yet), so you have to rely on keying it in exactly as listed. Like all the programs in the text, this one will look somewhat different on the screen or in a printer listing, since for clarity we have not reproduced the printer listings exactly, since printouts tend to contain broken words (when one line on the screen is full and the computer runs on to the next) and other possible confusions. Check each line carefully before you press NEWLINE (ENTER), and pay special attention to the punctuation. Notice that there are 2 spaces before the asterisk (spider) in line 50, and 3 spaces either side of the <=> (brick dropper/intergalactic space hod) in line 60. If you have any difficulty finding the right modes and keys for the characters you need, refer to the list in Section B (ZX81) and Unit W1 (Spectrum). It is very easy to end up typing a keyword instead of inputting it directly when you are keying in a listing (typing T,O instead of inputting TO, for example). If you do this it is not clear why you get the cursor indicating an error, since the line /ooks the same as the listing, so be warned. ZX81 Users! Notes The graphic character in line 160 is an inverse asterisk, (SHIFT B in Graphics mode) and in line 190 the characters are the SHIFTed graphic on the T key, the asterisk again, and the НІЕТеа graphic on the Y key. The comments in square brackets are intended to be helpful, not to be entered! Spectrum Users’ Notes Line 60 has an inverse video asterisk. Го get this, key CAPS SHIFT and the 4 key to get INV. VIDEO. Then input the asterisk. Use CAPS SHIFT and the 3 key to get TRUE VIDEO, i.e. normal black on 54 white, back. If you don't return to normal video, the quotes will be in Inverse, and so will everything after it. Line 190 has the unshifted G mode graphic on the 6 key, and then the CAPS SHIFT graphics on the 8 key and the 6 key as the graphics string. 5 КЕМ "BUG" 10 LET 5-0 20 LET B=10 30 FOR N-1 TO 12 40 LET C23 L SQ PRINT AT 2O»C-2;" +" [2 Spaces #] 60 PRINT AT (ЗЕ-2;" <=> и [3 5р, =>, 35 Sp] 70 IF INKEYS ="6" THEN GoTo 150 80 LET B=B+(3 AND INKEY$ -"&" AND B<28)-(3 AND ІМКЕҮФ = "=" AND B»3) 90 LET C=C+ INT ( ЕМО *2+1) 100 IF C<30 THEN GOTO 50 110 CLS 120 NEXT N ie ERE np 1g RER "9! — DSCUREDIEM % SRATI 140 STOF 150 FOR F=4 TO 20 ЕТЕР 4 160 FRINT AT Е,Б+1;"Ш" AT [Inverse %1 FsB*1;" " 170 NEXT F 180 IF E+1 <> C THEN GOTO 50 Г <> іс one character] 190 PRINT AT 20»C-1; "EF"; AT 2130-2; "SPLAT" 200 CLS 210 LET S=54+1 220 GOTO 120 When you've got it all keyed in, LIST it to check it through again. Check the first screenful, then (on a ZX81) LIST 170 to get the rest of the program (with a line that was on the first screenful to keep your place). LLIST it on the printer. Key RUN then NEWLINE (ENTER) to play. The keys 5 and 8 move you left and right respectively across the top of the screen. ‘They are chosen for the direction of the arrows printed on them. Key 6 will drop the brick. If you hit the spider it goes splat and you score a point. You have to hold the keys down to ensure that the computer will read the keys and perform the right operations. This is because it reads the keys only once in each pass through the loop (lines 50 to 100), апа might miss the input otherwise. When you’ ve played the game a few times, SAVE it on to tape and catalogue it. 55 | ——————— ph wrt - ot 740 | 7% 03: 2. -— ` 1484 4973 ^c, з I E á ja % “4: 5 i э pis * Ж | c ° m L 474 f ° I TL à é ” ' / F | L 1% и. i í í А б =, i ` Wf i r ; 4 ъ PART TWO ESSENTIALS OF BASIC PROGRAMMING SECTION G: PROGRAMMING METHODS I G1: Programming Now that you can operate your computer and have written a short program we must look in greater detail at the activity we call PROGRAMMING and study how: COMPUTERS SOLVE PROBLEMS To enable them to do this we engage in the two main activities of programming: 1 PRODUCE THE METHOD FOR SOLVING THE PROBLEM 2 PRODUCE A WORKING PROGRAM The method for solving our problem is called an ALGORITHM. An algorithm 1s like a cookbook recipe, and is written down in steps in a brief English style we call PSEUDOCODE, and the method by which we arrive at the recipe is called STRUCTURED PROGRAMMING. We break the problem up into smaller sub-problems or sub-tasks in a step by step, modular fashion, starting from the simple initial statement of the problem and working down to lower levels of greater complexity (i.e. in a TOP DOWN manner). As we refine our problem our steps become more like the operations the computer can perform. Our final description of the lower level of the algorithm will be in terms of the control and other structures of the language. To help us produce the algorithm we use STRUCTURE DIAGRAMS. The simplest of these is a TREE diagram. The pseudocode description of the algorithm is easily written down from the descriptions of tasks in the tree diagram. We cannot key the pseudocode description of the algorithm into the ZX81 or Spectrum because it will not understand it, and there is no means of doing it anyway. We have to translate each section of the pseudocode into its equivalent in the BASIC language, which the computer understands, to produce a PROGRAM. For the computer to be able to run the program successfully and produce the results we require, there has to be a LOGICAL FLOW to the program. This is often difficult to see from the structure diagram, and so we use another diagrammatic technique to illustrate the flow of control through the program, i.e. determine the order in which the program modules or sub-programs are processed and the order of coding the specific instuctions within a module. This technique uses FLOWCHARTS. These are important for documentation purposes and are in common use. We will describe them shortly. 59 Producing a working program involves running and DEBUGGING (correcting errors in) our first effort. We then have to TEST the program with sample data and finally DOCUMENT it. In this first section on methodology we shall consider problem solving and coding the algorithm in BASIC in more detail. You will see that the first half of the activity we call programming is LANGUAGE INDEPENDENT. Having produced our problem solving method - the algorithm — we can code it into any computer language we wish. We need to know the language thoroughly and how the fundamental programming structures we have used in the algorithm - decisions, loops, subroutines, subprograms, functions — can be implemented in that version of the language which runs on the computer we are going to use. In this book we are using the ZX81 or Spectrum computers. The versions of BASIC are slightly different. All that this means is that whilst the algorithms to be coded for both machines will be the same, the final programs may be slightly different. Our algorithms and their representation in pseudocode and flowchart form are thus PORTABLE from one machine and language to another. Good coding habits are also important. There are good and bad ways of turning the solution to a problem into a working program. Style, presentation, ease of understanding, modularity, efficiency are all important. Throughout our book the emphasis will be on correct problem solving techniques and good programming practice, while you gain a thorough knowledge of BASIC. Here is our first rule of programming: PROGRAM CORRECTLY FROM THE START Remember - bad habits die hard! The material in this Section may initially appear dense and difficult to follow. Work through the text carefully, and refer back to this Section as often as you feel necessary, when each of the topics covered in the following Sections (dealing with the essential groundwork of the BASIC language) has been introduced. The exercises given in the text should be used to put into practice both the specific techniques involved and the general approach to programming presented here. G2: Problem Analysis Producing the algorithm, or method of solving the problem, is often the most difficult part of programming because it involves the most work. From the start careful planning and organisation are absolutely essential. The task is simplified when a structured design method is used, coupled with a diagrammatic representation of the algorithm 60 using a structure diagram or flowchart. The actual coding of the program in BASIC using the available language instructions is then a straightforward matter. To produce the Algorithm we must: STATE THE PROBLEM RESEARCH THE PROBLEM DESIGN THE ALGORITHM DESCRIBE THE ALGORITHM IN PSEUDOCODE AND FLOWCHART FORM = һі = = A GO м м Let us now consider each of these steps. 1.1 State the problem fully 1.1.1 STATE THE PROBLEM 1.1.2 UNDERSTAND WHAT IS TO BE DONE To solve any problem we must know what the problem is and what is to Бе done. We later work out how to do it. A complete statement of the problem should include: (i) What information or data is to be input. (i) What answers or results are to be output. (uni) What operations аге to be performed on the data. At this stage a precise description of (111) may not be available. EXAMPLES Problem: Write a program which will print out the sum and average of five numbers input at the keyboard. Problem: Using the computer produce a telephone directory to contain up to fifty entries, which may be updated and assessed in an enquiry mode. In the first problem the input data, output data and operations are easy to see. The second is much more complex and needs more researching and information. What we are trying to do in 1.1.1 and 1.1.2 is to initially specify the problem as exactly as possible. When we analyse the problem further we may have to go back and ask for more information 1.e. a more detailed specification. 61 1.2 Research the problem 1.2.1 RESEARCH AND ANALYSE THE PROBLEM TO SEE HOW THE COMPUTER CAN HANDLE IT 1.2.2 IDENTIFY ALL FORMULAE AND RELATIONS INVOLVED 1.2.5 IDENTIFY ALL DATA INVOLVED Here we start to determine how the computer may solve the problem. We need to find out and write down: (1) What formulae and expressions are to be used. (п) What kinds of data are involved - numeric, string, etc. (ui) What functions are involved. (iv) What is input and output data. (v) What is the form of this data. (vi) How much data there is. (vii) What processing is to be done and how many times. It is useful at this stage to start to create a data table (a table of variables, constants and counters), to record how we are going to store the data. Other questions we will ask when we are a little more experienced are: Have I solved a problem like this before? Can I use my solution or modify it? Has anyone else solved it? Where can I find their algorithm or program? ALL THE FACTS OBTAINED FROM RESEARCHING THE PROBLEM SHOULD BE JOTTED DOWN We can now begin to design the algorithm in a structured manner. 1.3 Design the algorithm using structured methods 1.3.1 BREAK THE PROBLEM DOWN INTO SUB-PROBLEMS 1.3.2 USE A STRUCTURE OR TREE DIAGRAM TO HELP 1.3.3 CLASSIFY MODULES OR PART MODULES AS — INPUT — PROCESSING – OUTPUT USE FUNDAMENTAL CONTROL STRUCTURES SET UP A DATA TABLE REFINE THE ALGORITHM UNTIL CODING INTO BASIC IS AN OBVIOUS EXERCISE кі = = 92 G3 Go HD Qv > Structured programming means designing the algorithm in a top 62 down, modular fashion, with step by step refinement of the solution starting from the single statement of the problem which we place at the highest level. We break the problem into sub-problems at successive lower levels. Each sub-problem or module is one that can be solved individually. Structure diagrams or tree diagrams are useful as a representation of this refinement process. G3: Structure diagrams These enable us to break down the problem into distinct tasks and sub- tasks which eventually become simple enough to be coded directly in BASIC instructions. One form of these diagrams is TREE DIAGRAMS. The tree diagram has its trunk at the top of the page. We call this BOX 1 and give it the title: TASK TO BE DONE. We could have called it ‘problem to be solved’. For example, make a cup of tea or find the average of five numbers. We next break down the task into things to do. These are sub-tasks and each has its own box. For example: BOX 1.1: First thing to do BOX 1.2: Second thing to do Each sub-task is broken down into further sub-tasks: 1.1.1, 1.1.2 etc, each with their own boxes, the things to do placed in them becoming progressively more exact and simple. Breaking down a task into a tree diagram: first level second level її 1.2 145 FIRST THING SECOND THING LAST THING pO TO DO third level ERE И Е. 1.2.1 1.2.2 3.253 4,2,2 L. 39 Sub- Sub- Sub- Sub- Sub- Sub- Sub- task task task task task task | task The sort of programs you will start to write in BASIC are sequential, that is to say things are done one after another, so you need to be able to indicate that the program should first do one thing, then a second, then a third . . . and so on. You do this by drawing the boxes which 63 contain the tasks to be done in a straight line across the page next to each other for example: The numbers contained within each box identify where the box is placed on the tree. Take for example: The first digit shows it comes from the first level 1 ‘What is to be done’. The second digit ‘2’ shows it has come from the second level box 1.2 ‘Second thing to be done’. The third digit ‘3’ shows this box is the third sub-task in the sequence derived from which in turn is derived from . Into the boxes go brief statements of the actions needing to be performed. These are general statements at the top of the tree, e.g. ‘Get Sum of numbers’, but become more specific at each lower level, so that ‘Get Sum’ is broken down in the operations needed to produce the result ‘Get Sum’, e.g. ‘Input first number’, ‘Input second number’, ‘Add the two numbers’. Finally the instructions become detailed enough to form our English language ‘pseudocode’ which can be written out, ready to be translated into BASIC instructions. AN EXAMPLE OF TREE DIAGRAM DESIGN Here is an example to try out. Suppose we have a robot with arms, legs and eyes which we want to program to make a pot of tea. Our major task for the robot is: 1 Make а Pot of Tea This can be broken down into sub-tasks which we put in order across the page: 1 МаКе а Ров of Tea Les Put Water in Pot Each of these sub-tasks is still far too complicated for our robot to do. We must break the problem down further. Breaking down 1.1 into sub- tasks we get: те Ме 1.1.2 11.3 Fill the Kettle Plug in Kettle Wait Until with Water and Turn On Water Boiling The robot also needs to be told how to fill the kettle so we break this down as: 1.2.1 Fill the Kettle with Water у 9000. Т МИК: Wait Until Full L. L La L Put the Kettle Under Tap On the next page is a complete tree diagram. Certain things are still wrong with this algorithm for our robot, but it does show you how a problem can be broken down. G4: Classifying Program Modules Most computer programs involve: INPUT PROCESSING and OUTPUT activities. As we are designing our programs and forming modules, it becomes evident from our pseudocode description of the algorithm which of the above functions the modules should have. Depending on the problem and the result of our algorithm design, modules may be separately 65 99 T La Boil Water Put Tea the Pot Loan әш, Wait Get Tea Until Pot Water Boiling i E: Put Water into the Pot Lk ЖЕ! Take the Pot to the Kettle designated input, processing, and output functions or may have these functions nested as sub-modules. Module 2 PROCESSING Module OR Module І Module 2 PROGRAM G5: Control Structures PROCESSING OUTPUT Control structures are the statements or groups of statements (modules) in a program and algorithm by which the order of processing is controlled. Using them properly is the most important part of programming. BASIC is a line numbered language. The order of processing in a program is from the lowest line number in the program sequentially through to the highest, unless this is changed by using a control structure. Control structures link the different modules in a program together and are themselves modules. They will be dealt with in depth in the remainder of this section. To make our algorithm language-independent we can write them using a standard notation in pseudocode for the particular control structure together with its flowchart description. When we code the structures into the BASIC language the instructions used and the order of statements in the structure may be slightly different according to the version of BASIC and how ‘structured’ it is (i.e. how easily it accommodates these control structures). The structures we will study in BASIC are: (i) DECISION STRUCTURES (ii) TRANSFER STRUCTURES (iii) LOOPS (iv) SUBROUTINES (v) NESTED STRUCTURES (vi) SUB-PROGRAMS 67 DECISION STRUCTURES Computers make decisions by comparing the value of one variable against another. For example: IF А-0 THEN (do something) IF AS = “YES” THEN (do something) To make decisions they use relational (or conditional) and logical operators, like the equals operator above. Sinclair BASIC uses three decision structures: Simple decision Double decision Multiple decision As a result of these decisions control may be transferred to another program module, or local processing within the structure may take place. TRANSFER STRUCTURES These structures involve: (i) UNCONDITIONAL TRANSFER which is a direct transfer of control using a GOTO (line number) statement. Transfer is to another program statement or a module consisting of a group of statements. GOTO is a very powerful structure and must be used with care. (п) CONDITIONAL TRANSFER in which transfer of control to another segment is made as the result of a decision: i.e. IF (condition is true) THEN GOTO (line number). These program structures are discussed further in Section H. LOOPS The need for the repetition of simple tasks is one of the fundamental reasons computers exist. Loop structures are incorporated in most computer programs. A loop is a sequence of repeated steps in a program. This repetition must be controlled. We shall see in Section L that repetition is controlled by: (i) COUNTING (ii) TESTING FOR A CONDITION 68 There are three common loop structures: (i) Repeat (the process) forever! (ii) Repeat (the process) until (a condition is met). (ui) While (a condition holds) repeat (the process). Structure (i) is of little use, except that we have to note it and make sure it does not occur. In structure (11) the condition is tested after processing. In structure (iii) the condition is tested before processing. Sinclair BASIC uses a convenient and powerful set of statements for controlling repetition by counting called: FOR - NEXT Statements SUBROUTINES Structured programming involves breaking down а complicated problem into subproblems which can be worked on separately. SUBROUTINES are such separate independent program modules. They are distinct from SUBPROGRAMS which have similar properties in that they are routines or groups of program statements that are repeated more then once during a program run. Subroutine modules have a unique address and can have a name (like a person who lives in a house). Transfer of control to the subroutine from the MAIN PROGRAM, when the program runs is by reference to the subroutine address through a special SUBROUTINE CALL INSTRUCTION. This is the GOSUB (address of subroutine) statement. A return of control to the main program to carry on processing from where it left off is through a special instruction: RETURN. Subroutine structures in Sinclair BASIC are explained in Section N. NESTED STRUCTURES These are program modules or structures that lie entirely embedded within each other (like a set of Russian dolls). A simple nested structure 1s MODULE 1 MODULE 2 MODULE 3 69 In terms of program statements this would look like: module 1 Inn 222 s, 20 module 2 40 . — BE ыз шч module 3 SEL CIIM 2 80 IUD Ш. 120. — ——— ГІП... 140. 1. The flow of control is: START MODULE 1 TRANSFER CONTROL ——— 9» START MODULE 2 TO MODULE 2 TRANSFER CONTROL —————» START MODULE 3 TO MODULE 3 ү? COMPLETE MODULE 3 TRANSFER CONTROL BACK TO MODULE 2 COMPLETE MODULE 2 TRANSFER CONTROL BACK Subroutines, subprograms, loops and decisions may be nested in programs. Nesting is dealt with more fully in Sections H, L and N. G6: The Data Table When designing a program it is important that our knowledge of the data and information pertaining to the problem is complete. All data will need to be assigned a VARIABLE name, unless it is a numeric constant used in a formula. 70 The variable type will be either: NUMERIC - numbers - A, N1, COUNT, A(I,J) STRING -characters - A$, AS(I,]J) LOGICAL - numbers or characters - A, A$, NOT B Numeric variables will be integers, fractions, real and imaginary numbers. Strings will be names, characters and symbols. Logical variables will be the values TRUE or FALSE, 1 or 0 as appropriate to their use. Logic is dealt with in Section R. We also require to know whether our data is: INPUT OUTPUT or INTERMEDIATE Intermediate data is used in the body of the program, e.g. the value of a loop counter, or the intermediate result of a calculation. Intermediate data is useful for testing and debugging purposes when running the program or algorithm, using machine or hand traces. The equations, functions and expressions that will use the variables will need to be known. When dealing with equations, functions and expressions the units of the variables or parameters concerned must be known and should be stated. The first and simplest data table to construct is a descriptive list of variables to be used in the program. This is important for documentation purposes. For example: VARIABLE DESCRIPTION ITPR A First number Input B Second number Input SUM Sum of A and B Output A$ User response to Input ‘RUN AGAIN?’ For program design purposes the value ascribed to each variable at different points through the programs can be added. This forms a data table that is useful for checking the algorithm before and after coding it into BASIC, and is also a way of analysing errors in your own program, and understanding how other programs work. 71 ALGORITHM VARIABLES MODULE N N. 1 Loop counters are included in the list of variables. If their values are used for calculation inside the loop, this should be stated. There are some examples of this type of data table in the text. REFINING THE ALGORITHM The tree diagram should be further broken down and refined until the final sub-modules correspond to recognisable BASIC statements and structures. As you get more experienced, you will recognise more complex structures, and the solution to a problem wil become apparent at an earlier stage. G7: Describe the Algorithm 1.4.1 WRITE OUT YOUR METHOD OF SOLVING THE PROBLEM (THE ALGORITHM) IN STEPS ІМ А SIMPLE ENGLISH STYLE (PSEUDOCODE). 1.4.2 DRAW A FLOWCHART SHOWING HOW THE PROGRAM WILL RUN FROM START TO FINISH. 1.4.3 TEST THAT THE ALGORITHM WILL WORK BEFORE CODING IT INTO BASIC. Having broken our problem down into distinct things to do, or subproblems, to a stage where we are able to write a BASIC program, we need to do at least two things before we code. These enable us to write programs that work and that other users can understand. The algorithm description in pseudocode or flowchart form is an important point of the documentation of your programs. This is not written as part of the program but as a separate document which will also include a listing of the program. This is important for other programmers who may want to modify your program or use it as part of a larger program, and for you yourself if you come back to it after a 72 period of time and cannot remember how you designed it! The program listing alone is often not enough, if the algorithm is complex, to show how the program works. G8: The Pseudocode Description In the structure or tree diagram - which we draw out in rough on a piece of paper as we design our solution — each block or module right down to the lowest level has an English description of the task to be done inside it. (The very lowest level tasks will be described in sentences that are very similar to the BASIC program statements themselves, as you will see in Programming Methods II.) Our algorithm will be written out, in a step-by-step fashion, and will include all the descriptions in the boxes. The highest or first level description (simple box) will be the algorithm and program title. The second level will be the titles of the program sections. Each of these major sections will encompass a further group of modules, all of which will be named in our description of the solution. The lowest level of our tree diagram will be the specific instuctions the computer has to perform. These will be translated into the BASIC language on an almost one to one basis, and will contain the important and easily recognised language structures, for making decisions, branching and jumping, and repetition that we have previously mentioned. (A summary of pseudocode descriptions of some control structures and their flowcharts with BASIC program equivalents is given in Section 0, Programming Methods II.) If you imagine turning the tree diagram on its side and taking away the boxes, the descriptions that are left constitute a pseudocode description of the algorithm. As an example, let’s look at the tree diagram and the algorithm description for the problem of asking our robot to make a pot of tea. Using our tree diagram we can write down our algorithm for making a pot of tea as a sequence of instructions (to be coded later into a computer language). We use the English language as our pseudocode and our program is written directly from the sub-tasks in the bottom line of boxes in the tree diagram. We use the boxes at higher levels in the tree to define distinct modules. Comments or REMARK statements identify each module and explain what is being done in each algorithm section: Remark * * Algorithm for robot to make pot of tea * * Remark * Boil water - task 1.1* 1,4,4 ЕШ the Кеше with water 1,1-4 Walt until the water is boiling 1.3 Plug in the kettle and turn it on Remark * End of task 1.1* Remark* Module - Put tea in the pot — task 1.2 * Ix Get toe pot 1.2.2 Put 200 tea bags in the pot 73 Remark” Епа of task 1,2% Remark * Module - Put water in the pot - task 1.3 * 1,2,1 Take pot to kettle 1,2,2 Stir tea with spoon 1.54 Put lid on tea pot Remark * End of task 1.3 * Remark * * End of Algorithm - tea is made * * You can see that the tree diagram shows why each part of your algorithm is included and why it is in the particular position in which you have placed it on the tree. The tree diagram contains information about three things: (1) The problem broken down into different levels of detail starting from the general concept of what is to be done down to the specific activities and instructions which will enable the problem to be coded. (2) ‘The order in which instructions must be performed. (3) The comments which must be included to explain what the program is doing. Exercises 1 Our algorithm has the following mistakes in it: a) Some instructions are wrong. They are spelt incorrectly and the robot will not be able to recognise them. b) Some instructions are in the wrong order. c) Some instructions are missing in the algorithm. d) Some instructions are missing on the tree diagram. Find the mistakes! 2 Correct the tree diagram and the algorithm. 3 Expand the tree diagram and the algorithm to a further sub-task level. For example: „л Fill the kettle becomes 1.1.1.1 Put kettle under tap 1.1.1.2 ‘Turn on tap etc. 4 Draw а tree diagram and write the algorithm in pseudocode for a robot to set up and switch on your microcomputer system. G9: Flowcharts Flowcharts are a second graphical method used in designing programs. They consist of linked boxes of different shapes. Each shape has a different use and, as with tree diagrams, each contains a brief description of what the program should do at a particular point. It is harder to design programs using flowcharts than with tree 74 diagrams. Their power comes from using them to help make visible and describe the flow of control in the algorithm and the resulting program. They are used to help code the program into BASIC instructions, and later form an important part of the DOCUMENTATION оға program. Note that flowcharts express the important control structures used in programming in diagram form. We give a selection of standard flowchart symbols here. There are additional ones, but their usage varies. The conventions of use should be followed if you wish other people to understand your flowcharts. For your own use, in analysing programs, you may be less exact, but not less systematic. Flow in a program can be illustrated by a selection of blobs and rectangles only, given that the lines of flow are correctly given, and the right words are written in the blobs! Doing this is all right for yourself, but not if your flowcharts are to be comprehensible to others. FLOWCHART SYMBOLS Flow lines. These connect the program blocks. Y “pes The arrows show the direction of flow, and are very important. This symbol represents any kind of processing function, that is general Programming dinis Statements, i.e. ''Purchase Tea'' or LET A- В + С. This represents а decision, with а Conditional — test, e.g. “Is there another shop open” or <> IF A=3 THEN ... It has a Yes/No branch, No according to whether the condition is True or False, which determines the program flow. This represents either Output in the program m" to the screen or printer, or Input from the keyboard, e.g. PRINT “HAVE YOU A PACKET OF TEA?” or INPUT B. This represents a named process that is specified elsewhere, e.g. Subroutine GOSUB 1000. The subroutine would have a separate flowchart. 75 This represents an exit to or entry from another part of the flowchart, allowing one part of the chart to be connected to another part. Used when another direct line link would be confusing, or to connect to a separate page. This represents the Crossing of two Flow Lines. They are not connected. This represents the Junction of Flow Lines. The two lines of flow join. STOP Terminal Point, e.g. Start, Stop, Pause. A flowchart does not branch out like a tree diagram. It always converges to the stop point. It has a direct relationship to the program it describes. Writing down a flowchart is rather like drawing a diagram of the program itself. Below are some examples of simple flow structures, with the program and the flowchart. FLOWCHART PROGRAM 1. Simple sequences 10 LET X = 5 20 INPUT Y 30 PRINT X,Y FLOWCHART PROGRAM 2. Decision and program branch 40 IF Y-0 THEN GOTO 70 50 LET X=100 60 GOTO 80 70 LET Х-0 80 PRINT X 90 STOP Notice that we have omitted a flowchart symbol for line 60. This GOTO is indicated by the flow lines. The same is true of the GOTO in the conditional statement of line 40. 10 INPUT X 20 IF X-0 THEN GOTO 50 30 PRINT X 40 GOTO 10 50 REM **END** PRINT X 77 : Notice that the above flowcharts represent the programs line by line. Flowcharts can also be less detailed, and the flowchart symbols used to represent program blocks (sequences of program instructions) or modules rather than one or two lines. They then describe a less detailed flow structure. We might have a flow that was represented like this: INSTRUCTIONS INPUT 10 NUMBERS FIND SUM, AVERAGE This is like a flowchart of a higher (less specific) level of a tree diagram. Each section could have a more detailed flowchart drawn up to show the individual lines of the program, or comments could be added to the blocks above, relating the program lines to the blocks: 78 INPUT Input loop in lines 10 а Г 40 t NUMBERS o 69 You will soon start to write short programs, and should draw up flowcharts with each program line or instruction indicated separately. Later, for longer programs with large numbers of lines, the flowcharts must be condensed where the sequence is simple to follow in the program, to keep them of manageable size. Any complex manipulations should still be included in full. EXAMPLES (1) Here is a flowchart for our robot. We are going to ask it to buy a packet of tea. ENTER SHOP HAVE YOU A PACKET OF TEA LS THERE ANOTHER SHOP PURCHASE TEA 79 In the same way as our ‘making a pot of tea’ problem which the robot has to solve, each of these boxes must be broken down into simpler instructions. On a simple flowchart it may not be possible to see how the problem has been broken down. What we must do is either draw the whole flowchart again with more detail or draw new expanded flowcharts at specific points, e.g. “ENTER SHOP” could be replaced with the following: 80 (2 Here is a flowchart of a program to input two numbers, output the sum, and ask you if you want to run the program again. 81 INPUT À INPUT B LETS = A+B PRINT S PRINT ‘‘RUN AGAIN? (ҮЕ5/МО)” INPUT A$ IF A$ = ‘‘YES’’ THEN GOTO 10 STOP AN EXAMPLE OF STRUCTURED DESIGN Problem: Find the average of five numbers: (1) TREE DIAGRAM Find Average of 5 numbers Get each Set counter number, add Find Print & sum to Q it to the sum Average Average Let Sum = Let Counter Add 1 Input to counter number End of summing if counter = 5 Let Let If Counter Let Print Counter = Sum = = 5 then Average Average Counter +łŁ Sum+X end summing =Sum/5 (2) FLOWCHART START SET COUNTER -0 92 ADD COUNTER Note that the flowchart and program test whether the counter value is less than 5, using the < symbol. (3) PROGRAM REM “AVERAGE” REM ** PROGRAM FINDS AVERAGE OF FIVE NUMBERS INPUT ** REM ** START ** LET SUM = 0 LET COUNTER = @ LET COUNTER = COUNTER + 1 INPUT X LET SUM = SUM + X IF COUNTER < 5 THEN GOTO 60 83 100 LET AVERAGE = SUM/5 110 PRINT AVERAGE 120 KEM ** END ** The operand “” means ‘divided by’ and is equivalent to the ‘+’ symbol. Exercises 1 Design an algorithm (using tree diagram) and write a BASIC program with a flowchart to find the sum and average of ten numbers to be input at the keyboard. 2 Produce the tree diagram, flowchart and program which calculates the area of any rectangle. 3 Design the algorithm, BASIC program and flowchart which calculates the total volume and weight of three boxes to be airfreighted from London to New York. Use the following data: BOX LENGTHCM BREADTHCM HEIGHTCM WEIGHT KG 1 20 4 2 2 2 40 3 6 2.5 3 70 10 15 20 Test that it works! G10: Testing the Algorithm It is always best to make sure your method of solving the problem actually works before coding it into BASIC. This pre-coding check is known in the programming trade as a DRY RUN or WALK THROUGH. Using the DATA TABLE, we check through, module by module, the values of all the variables, expressions and counters step by step through the algorithm. This will uncover errors in the logic and method and will save time when debugging the finished product later on. Professional programmers always do this as they have to work to very tight time schedules, and by doing things properly at the start they save time later on. We would like you to try a few walk throughs on the simple programs you will be designing at first, just to get the hang of the idea. We have now covered the first essential steps in designing a program and have seen a simple coding process. We have talked about methods and concepts and introduced some new terminology. After concepts we go to detail. The algorithm is ready to be coded into a BASIC program. In doing this we are going to put into the program the fundamental programming tools, which are language structure and control structures. We have to know what these structures or tools are before we can use them. This requires a look at how Sinclair BASIC, through small groups of instructions, enables decisions to be taken, branching 94 and jumping to different parts of the program to happen, repetition of parts of the program to take place and how separate modules called subroutines and sub-programs can be called into action where necessary — these are the language structures. Let’s go and meet them! 85 SECTION H: CONTROL H1: Control in Programs The statements which make up a BASIC program are numbered. BASIC is thus called a LINE NUMBERED LANGUAGE. Control in all BASIC programs is carried out by reference to these line or statement numbers. The ZX81 and Spectrum will normally run a program from the lowest numbered statement through to that with the highest number unless instructed to do otherwise. This is exactly what concerns us here, and thus we need to recognise that we can control the order in which program statements are executed by using four important instructions in Sinclair BASIC: - GOTO (for direct transfer) - IF-T HEN (for decisions and branching) - FOR-NEXT (for loops (repetitions)) - GOSUB-RETURN (for accessing program modules called subroutines) These instructions are used singly or combined together with other instructions to form groups of program statements called CONTROL STRUCTURES. There are four principal control structures: - DECISION AND BRANCH - LOOPS - SUBROUTINES - NESTED STRUCTURES In this Section we will discover how to take decisions and branch to other parts of the program. We will study the remaining structures later in Part Three. The most important property of a computer is that it can be programmed to make decisions, by using the relational or conditional operators of BASIC. H2: Condition Testing CONDITIONAL OPERATORS Conditional operators are also called relational operators as they determine the logical relationship between two expressions, numeric or string, as: Equality: = Inequality: «<> Greater than: > Less than: < Greater than or equal to: >= Less than or equal to: < The priority of conditional operators is 5. Priority will be explained in Section J. They are executed in order left to right across a statement unless in brackets. We often need to use the complements or opposites of these operators in decision making. The complements are: Operator Complement equality = inequality <> greater than > less than or equal to < = greater than or equal to > = less than < The reverse operations are true in each case. H3: IF-THEN IF-THEN Conditional operators are used with: IF-THEN statements IF (CONDITION IS TRUE) THEN (PERFORM AN INSTRUCTION). For example: 40 IF (А = B) THEN GOTO 10 50 IF C <=6 THEN STOP 60 IF J > K THEN PRINT “J” The format of the statement is: IF (CONDITION) THEN (INSTRUCTION) Any BASIC instructions can be used in this kind of statement, although a number are unlikely to be useful (e.g. NEW, CLEAR). In general if the condition in the program line is TRUE then the instruction following the condition is obeyed. If the condition is not TRUE (FALSE) then control passes to the next line. This powerful facility enables us to branch and transfer control to another line in the program. IS YES BRANCH THE CONDITION (TRUE PATH) TRUE? NO BRANCH (FALSE PATH) GO TO THE NEXT LINE 87 H4: GOTO [Instructions GOTO The normal control sequence in a program is via numbered statements — from the lowest to the highest. GOTO (line number) switches control to the line number specified: 100 GOTO 20 200 GOTO (B + C) As a command GOTO 30 executes a program from line 30. Unlike RUN, with this method variables are not cleared before execution. The Spectrum includes a space between GO and TO when printing this instruction. Exercises Key in and run this program which checks that only positive numbers are input and gives a bad data error message as well as prompting for the next input. Notice the use of IF-THEN and GOTO. INPUT both positive and negative numbers. 10 REM*INPUT CHECK* 20 INPUT A 30 IF A»0 THEN PRINT A 40 IF A«-0 THEN PRINT "BAD IN PUT" 50 PRINT "HAVE YOU ANOTHER NUMB ER? ANSWER YES OR NO" 60 INPUT AŠ 70 IF А5 ="YES"THEN GOTO 20 88 STOP 90 REM*END INPUT CHECK* Now try these exercises which demonstrate the power of GOTO: 1 10 PRINT “CENTURY”; 20 GOTO 10 Run this program 2 10 GOTO 80 20 PRINT “COMPUTERS'”'; 30 GOTO 10 40 PRINT ‘‘PERSONAL”’; 50 GOTO 20 88 60 PRINT ''SINCLAIR''; 70 GOTO 40 80 GOTO 60 Key it in and sort it out! This is called ‘spaghetti programming’. Structured programming techniques have been designed to avoid the excessive use of GOTO statements. 3 10 INPUT A$ 20 PRINT A$; 30 GOTO 10 INPUT some graphics characters and watch the patterns! 4 Кеуіп and run this example: 10 INPUT A 20 IFA = 1 THEN FORI = 1 TO 10 30 PRINT “CENTURY” 40 IF A=1 THEN NEXT I 50 STOP Line 10 asks you to input a number. Line 20 examines if it is equal to 1. IF this condition is TRUE then a FOR-NEXT loop is set up to print “CENTURY” ten times. If it is not TRUE then control passes to the next line. Line 30 “СЕМТГКҮ” is printed once. Line 40 the condition is tested again. If TRUE the loop continues and CENTURY is printed again. If not then control passes to line 50. Line 50 stops program execution. Can you understand it? If not wait until you have read the section on LOOPS. H5: Decision Structures DOUBLE DECISIONS The simplest decision involves the evaluation of a LOGICAL CONDITION - i.e. a condition that may have the value of either TRUE or FALSE. A result of this evaluation decides which part of a program is executed next. These parts of the program are called TRUE TASK and FALSE TASK. 89 The flowchart for the Double Decision STRUCTURE is: It is called a double decision as there are two alternative modules that can be performed. In the flowchart, if the indicated condition 1s true, then the program section representing the True task is carried out, otherwise the program section representing the False task is performed. Only one of the paths from the condition test is taken, and the program will continue at the statement represented by the arrow at the bottom of the flowchart. Each task can be a single instruction or a statement or a group of instructions. The Double Decision Structure is known by the general name of the "IF-THEN-ELSE Decision Structure’’. Its general form 1s: IF (condition) THEN (true) ELSE (false) This means: IF the condition tested is True THEN perform the True task, and IF the condition is not true perform the False task. Our algorithm description of it would look like: 1. Decision Module. 1.1 Do the test. If result is True then 1.22 По True task 1.3 Otherwise do False task We can write this formally in pseudocode as: 90 module - decision if condition then True Task else False Task end if end module End if and end module are bounds to the structure. In Sinclair BASIC we code it as: 10 IF (cond) THEN (branch to True task) 20 (False task) Note that in this case the only literal equivalent of BASIC from the pseudocode is with the use of IF and THEN. The branch to the true task is made with a GOTO instruction. For example: 10 IF A»0 THEN GOTO 100 20 REM * FALSE TASK * ЗӨ uus 90 GOTO 120 100 REM * TRUE TASK * 110 PRINT A If we did not branch to the true task starting at 100 and used: 10 IF A20 THEN PRINT A 20 REM FALSE TASK in line 10, the true task would be processed and control would then pass to line 20 - the false task. In other words, both tasks would be processed! Watch out for this. EXAMPLE: Input two names as strings. The program compares them and prints them out in alphabetical order: 91 14 REM * ALPHA * 20 INPUT A$ 30 INPUT B$ 40 IF A$<B$ THEN GOTO 80 FALSE 50 PRINT B$ TASK 60 PRINT A$ 70 GOTO 100 TRUE 80 PRINT A$ TASK 90 PRINT B$ 100 STOP 110 REM * END ALPHA * THE SINGLE DECISION This is a special case of the double decision structure in which there is only one task to perform - the True task. TRUE TRUE TASK This is called an IF-THEN decision structure. Its BASIC form is: IF (Condition) THEN (True) Which means: IF (the condition test is true) THEN (perform the true task) Our algorithm description would be: 1. Decision module 1.1 Perform test 1.2 If True, process true task 92 A brief formal pseudocode description is: mod - Decision if Condition Then P end if end mod Our BASIC statement is: IF (condition) THEN (TRUE) EXAMPLE: Input numbers and stop if a number greater than 10 is input: 10 INPUT A 20 IF A>10 THEN STOP 30 GOTO 10 5ТОР Note the abbreviation of True to Т апа False to F. MULTIPLE DECISIONS There is often the need in programs to perform several tasks based on the result of a set of conditions. To solve these problems we use a 93 multiple decision structure. This kind of structure is especially useful in breaking up larger tasks into smaller ones. Multiple decisions are most conveniently handled by multiple logical operations. This is covered in Section R. We will consider the conventional way of handling them. As an example of multiple decisions consider a food vending machine. You put a coin in and press the respective button of the article you wish to be delivered to you. Another example would be a set of arithmetic testing programs, with questions in each. The computer would ask you which set of tests you required, you would key in the reply and, from several alternatives, the required program would run. The flowchart for such a structure is: START Where C1, C2, C3 are the conditions and Р1, Р2, P3 are the True tasks. EXAMPLE: Input any of three letters A, B, C and print out a corresponding reply. = FRINT "ENTER AoE üR C" 10 INFUT ñ$ 20 IF АФ-"А" THEN GOTO 60 94 30 IF А%Ф-"Е" THEN GOTO ЕО 40 IF AS="C" THEN GOTO 100 20 STOP 60 PRINT “YOU INFUT A" 70 STOP S0 FRINT “YOU INPUT Е" 90 STOP 100 PRINT “YOU INPUT C" 110 STOF The Pseudocode description of this structure is: case if Cl then P1 10 IF (C1) THEN (P1) if C2 then P2 20 IF (C2) THEN (P2) if C3 then P3 30 IF (C3) THEN (P3) endcase endmod PROGRAMMING WITH GOTO When programming in BASIC take great care in how you use the GOTO statement. It takes two main forms. Used on its own it 1s called an unconditional GOTO and when used with IF-T'HEN it is called a conditional GOTO. GOTO enables you to jump around in a program like a flea on a blanket - don't do it! Try and code your program to execute in sequence and avoid it becoming a bowl of spaghetti. Excessive use of GOTO makes programs difficult to refine and debug. Relationships between the program paths become difficult to follow. However — do not take the other extreme and write awkward complicated code to try and avoid GOTOSs! Ideally, unconditional GOTO statements should only be used to skip over code and not to repeat code sections (i.e. they should only be used to transfer control forward in a program). Do not put an unconditional GOTO inside a loop or subroutine to jump out of it. Do not jump inside a loop or subroutine, because you'll find that jumping in and out of loops can cause unpredictable results. Do not jump to another GOTO. For example: 100 GOTO 200 200 GOTO 300 95 or else 100 GOTO 100 ! Exercises 1 2 H6: L Write a program to input integer numbers and stop if zero is input. Write a program to input integers and count the number of times zero 15 input. Write a program to input integers and calculate the percentage of zeros input. Write a program which prints out the result of dividing any two numbers’ input and gives a “Һай data - try again” message if any of the input values is zero. Write a program which will print out on request a lunch menu for the different days of the week. ogical Operators: AND/OR We will only introduce you to simple logical operations here. Logic is dealt with fully in Section R. Use of the AND and OR statements enables us to combine conditional statements in powerful ways to make more complex decisio ns in programs. AND AND combines relations so that the expression: e.g. (condition 1) AND (condition 2) (A = B) AND (В>1) is TRUE when BOTH conditions are TRUE. It is FALSE when one or both conditions are FALSE. OR e.g. OR combines relations so that the expression: (condition 1) OR (condition 2) (A = B) OR (B<>1) is TRUE when EITHER condition is TRUE. It is FALSE when both conditions are FALSE. The expressions formed by the use of AND and OR are used with LE ua d. HEN statements. For example: 20 IF Х>1 AND X«10 THEN PRINT '* BETWEEN 1 AND 10” 96 50 IFX<>2 AND X<>3 THEN PRINT < A МОТ EQUAL TO 2 ОҚ” 40 IF A=B OR B=C THEN LET F=F+1 The first example will be true if X is greater than 1 and X is also less than 10, and the message will be printed. If X was 11, the first condition would be true, but the second false. The whole expression would then be false. Notice the danger with the second example, in that we say in English ‘not equal to 2 or 3’, but we must key in an expression using AND. It is clear once you realise that two conditions are to be tested — ‘not equal to 2 and not equal to 3’. If, for example, X were 3 when this line in the program was reached, then the second condition would be false in this expression, and the whole expression would also be false. The third example would be true if ezther A was equal to B or if B was equal to C. It is also true if both these conditions are true. We can also combine more than two conditions: 20 IF A=BANDB=CANDC = 20 THEN STOP will stop if all three conditions are true. If one or more is false then the whole expression is false. Similarly: 20IFB-20R B-3ORB-4THEN LET B- 1 will make B - 1 if B is equal to 2 or 3 or 4. It is also possible to use combinations of AND and OR: 30 IF (A = BAND B>2) ОК (A = 2 AND B = 3) THEN GOTO 60 The expressions in brackets are evaluated first. The first expression in brackets will be true if B is greater than 2 and equal to A. The second expression will be true if A is 2 and B is 3. The program will pass control to line 60 if either expression in brackets is true. To summarise: where T1, T2 etc. are true conditional expressions and F1, F2 etc. are false conditional expressions: (T1) AND (T2) TRUE (T1) AND (F2) FALSE (F1) AND (T2) FALSE (F1) AND (F2) FALSE (T1) OR (T2) TRUE (F1) OR (T2) TRUE (T1) OR (F2) TRUE (F1) OR (F2) FALSE Each condition may also be another AND or OR expression. Exercises Work out what will be printed by these programs, then key in and run them to check. The operator ‘‘/’’ means ‘‘divided Бу” (+) and “%” means ''multiplied Бу” (*). 97 Make sure you have got the programs correct before you run them. Work out both sides of each expression using a relational Then, giving each expression a T or F value, work out the bracketed AND/OR expressions. This gives you a T or F value for the whole bracket. Then work out whether the whole operator first. LET A=2 LET B=3 LET С-10 LET X=15 IF X/B=A AND C/A=5 THEN PRINT "LINE 50 TRUE" IF X/B-A OR C/A=5 THEN PRINT "LINE 60 TRUE" IF X/B=C/2 AND X>=15 THEN PRINT "LINE 70 TRUE" LET A-20 LET В-150 LET X=7.5 LET Y-2 LET 5-В/20 IF S=X AND X*A-B AND Y-2 THEN PRINT "LINE 60 TRUE" IF X-B OR X«20 OR X>2 THEN PRINT "LINE 70 TRUE" IF (X=7.5 OR Ү-10) AND (A/Y-1 @ AND В-150) THEN PRINT "LINE 80 TRUE" expression will be true or false. Write some similar programs for yourself to experiment with all the relational operators used with AND and OR. 98 SECTION I: PRINTING I1: PRINT LPRINT PRINT The PRINT statement is used to output information by displaying it on the screen. It can take many forms. For example: 10 PRINT A prints out the value of numeric variable A 20 PRINT B$ prints out string variable B$ 30 PRINT “YOUR NAME?" prints out whatever is included within the quotes (inverted commas) 40 PRINT (B**2 — 4*A*C) prints out the calculated value of the expression 50 PRINT leaves a blank line LPRINT The LPRINT statement is used to output information by printing it out on the printer. The LPRINT statement is used in exactly the same way as the PRINT statement, but produces printer and not screen output. If the printer is not attached LPRINT statements are ignored. The screen size for printing is 22 PRINT lines down the screen, and each line is 32 columns (character spaces) wide. The actual screen size is 24 lines by 32 columns, but the bottom two lines are reserved for commands and operating messages. The lines are numbered @ to 21 down the screen and the columns 0 to 31 across. The PRINT statements shown above each commence at the left-hand side of the screen, and each PRINT statement moves the printing position to the start of the next line after it prints whatever it was told to. Lines of greater than 32 characters will go on to the next line automatically. To clear the screen of printing we use the CLS (Clear Screen) statement. 99 CLS CLS erases all printing on the screen, and sets the new print position at the start of the top line of the screen. I2: Spacing Items on the Screen Е А semicolon (;) between two items causes the printing of the second item immediately after the first. For example: 10 PRINT A;B$ 20 PRINT “АУЕКАСЕ”;С Try the following program: 10 LET A=6.89 20 LET B=87.6 30 PRINT A;B 40 PRINT ''AVERAGE"'';(A + B)/2 The display is: 6.8987.6 АУЕКАСЕ47.245 This does not give а very satisfactory display since values run into each other. One simple way to overcome this is shown below. 10 LET A= 6.89 20 LET B=87.6 30 PRINT A;" "В 40 PRINT “AVERAGE ”;(А+В)/2 The display now becomes: 6.89 87.6 AVERAGE 47.245 ci A comma (,) between two items causes the print position to be shifted on (at least one place) to either column 16 or to the next line column 0. For example: 10 PRINT A,B 20 PRINT A$,B$ 30 PRINT “АУЕКАСЕ”,С Try the following program: 10 LET A= 7.65 20 LET B= 8.67 30 PRINT “AVERAGE” (А + B)/2 100 40 PRINT 50 PRINT ‘‘NUMBER!1’’,‘‘NUMBER2’’, “АУЕКАСЕ” 60 PRINT A,B,(A + B)/2 The display is: AVERAGE 8.16 МІ/МВЕК1 NUMBER2 AVERAGE 7.65 8.67 8.16 Clearly the comma is useful if we wish to print a table with two columns, but is unsuitable if we wish to have a table with more than two columns. It is important to remember the screen size when deciding the form of your output. For your output the effective screen is 22 lines each 32 columns wide. TAB TAB C; moves the print position to column C. If this would involve back-spacing it moves on to the next line. The following program (with printout) indicates how the TAB function can be used to improve the presentation of results. 10 LET А$ = “А.В.ЈОМЕЅ” 20 LET B= 65 30 PRINT “NAME”;TAB 6;A$; TAB 19:“АСЕ”: TAB 23;B;TAB 27; “YEARS” NAME A.B.JONES AGE 65 YEARS Note the semi-colons between TABs and print items. It is important to remember that each line has 32 columns, numbered 0 to 31. The next program shows a simple way of tabulating results. 10 PRINT “МО.”;ТАВ 4;“5ОСАКЕ”;ТАВ 12; “СІУВЕ”;ТАВ 20;*RECIP" 20 INPUT N 30 PRINT N;TAB 4;N*N;TAB 12;N*N*N; TAB 20;1/N 40 GOTO 20 101 NO. SOUARE CUBE RECIP 1 1 1 1 2 4 8 0.5 3 9 9/ 033333333 4 16 64 0.25 5 25 125 0.2 6 36 216 @.16666667 7 49 242 0.14285714 8 64 512 0.125 9 81 729 0.11111111 10 100 1000 0.1 It is important to remember that numbers are output with up to 8 figures and allow the appropriate space. An alternative is to decide how many figures you want and use the INT function (see Section J). I3: PRINT AT AT L, C moves the print position to line L and column C. For example: 10 PRINT AT 10,12“ CENTRE" will cause the string specified to be printed starting at line 10, column 12, i.e. roughly in the centre of the screen - since L goes from 0 to 21, counting down the screen, and C goes from 0 to 31, counting left to right. EXAMPLE The program below sets up a symmetrical pattern using the character of your choice. Note the use of the command CLS to clear the screen of your input. 10 PRINT AT 5,4;"WHICH CHARACTER?" 20 INPUT AŠ 30 CLS 40 LET L=INT (RND*10)+1 50 LET C=INT (RND*15)+1 60 PRINT AT 11%,,164С;А65 70 PRINT АТ 11-L,16-C;A$ 80 PRINT AT 114L,16-C;A$ 90 PRINT AT 11-L,16+C;A$ 100 GOTO 20 Try adjusting the parameters in lines 60-100. The important feature to remember is: Number of character cells is 32 horizontally by 22 vertically, i.e. 32 x 22 altogether. The TAB function uses C = @ to 31 only. The AT function uses L = 0 to 21 and C = 0 to 31. You should have noticed that the PRINT commands reinforce each other, and provide alternative ways of achieving the aim of placing characters, character strings or numbers at the desired positions on the 22 line, 32 column screen display. For example, these three programs: 19 LET X = 3 20 PRINT X,,;, 30 PRINT X*X 10 LET X = 3 20 PRINT X 30 PRINT 40 PRINT X*X 10 LET X= 3 20 PRINT X,TAB 32;" "TAB 32;X*X would give the same printout on screen. The number of keystrokes (count them) is what determines which statement usage is efficient in any instance. You will soon come to recognise which to use if you experiment. PRINT AT instructions will overprint anything already printed at the position specified. We can use this to replace on the screen one set of data, or one string, by another. 10 INPUT X 20 PRINT AT 0,0;X 30 GOTO 10 overprints one X by the next X each time. If we input 1,2,3...10 it works fine. But if we input 10,9,8...1 we get: etc. Similarly, ZU ЕТТІ” 40 PRINT AT 10, 10; “SINCLAIR” works, but not if we swap the two strings around - we end up with ZX81LAIR, and we have the same problem with numbers, which can be between one and eight digits long. We can blank out something on the screen by overprinting an empty string. For the simple problems above, the addition of appropriate 103 strings will work; we add 4 spaces after “27Х81”, so that line 10 becomes: 10 PRINT AT 10,10; “ZX81 E and for numbers, we can use: 20 PRINT AT 0,0;X; *“ id (7 spaces) Using LPRINT also requires care. For the LPRINT instruction, TAB works exactly as PRINT TAB. LPRINT AT L,C is converted to LPRINT TAB C, and the line number is ignored. This is because the printer cannot go back to a previous line. Try this program. Input 1,2,3,4,5. 10 INPUT X 20 LPRINT AT X,X;X 30 GOTO 10 will print 12345, as if line 20 had read LPRINT TAB X;X. For any programmed screen format that 1s not a simple sequence of print lines, it is better to use COPY to produce output on the printer, once all the data is on the screen. COPY prints the entire current screen display on the printer. If used as direct command, we can COPY less than a whole screen by pressing BREAK before completion, but if used in a program, the whole screen will be copied. 14: The Graphics Characters оп the ZX81* The ZX81 character set includes a set of graphics characters, and you were told how to access them in Section B. To recap: Graphics characters are accessed by using |Graphics| to get the cursor. Repeat to return to cursor. Unshifted keys then produce inverse video characters. (e.g. key Q gives |.) Shifted keys produce graphics cells, if shown on the keys: e.g. SHIFT R gives "W .If no graphics cell is shown, result is inverse video form of normal shifted character (e.g. SHIFT U gives В ). The inverse video characters and graphics cells can be used for enhancing displays and drawing bar charts, diagrams and pictures. They are manipulated as strings, by putting quotes round them, e.g. PRINT “ ER or PRINT “ B”. * The Spectrum offers more extensive graphics facilities than the ZX81, and Spectrum owners should refer to Unit W3 for details. The Spectrum has the solid graphics characters of the ZX81, but not the shaded characters, on keys 1 to 8 in graphics mode. Read through this section bearing this in mind. 104 Put your computer in graphics mode and run through the keyboard, noting the unshifted and shifted versions of each key. Note that RUBOUT (DELETE) works with the cursor, but the cursor control keys do not, and that the cursor must be on screen for them to work. By the time you fill one line and move on to the next, you will see that all these graphics characters Join up, with no gaps between the cells. The difference between the grey cells on the A and K keys is that they Join up with the half-shaded graphics cells on the S, D, F and G keys in different ways. Experiment with these. If they join up properly, you cannot see the Join. If they do not, the Join is visible as a chequered pattern. To check the characters across the screen, use the bottom lines of the screen directly. To check the vertical Joins, enter this program: 10 INPUT A$ 20 PRINT A$ 30 GOTO 10 Change the cursor to [G], then input the graphics character. You have to then press NEWLINE (ENTER) twice; the first time to change to [L], the second to input the character. We can use the graphics characters to draw (crude!) pictures, enhance printout on the screen — by printing prompts in inverse video for example —or putting titles inside surrounds, and use them in diagrams or moving graphics. You'll have to wait a few more chapters before we can do anything interesting, but here are a few things to try: Here’s a program to put a border round a word in inverse video. Notice we store the graphics in string variables. This gives us better manipulative power than if we just used literal strings. On the ZX81 the graphics characters in A$ are the shift graphic on the E key, 11 times the one on the 7 key and the one on the R key. If you are using a Spectrum, the relevant keys are ‘4’, ‘3’ and ‘7’. You can work the other lines out for yourself. A s ie zu зә 46 i се e Notice the combined PRINT AT statements in line 60. The production of inverse characters on the Spectrum (white characters on a black background, unless colour is being used) can be done in different ways. You can use CAPS SHIFT and the 4 key to put an INVerse VIDEO control character before a letter or other character, but this will make a// characters thereafter into their inverse forms unless CAPS SHIFT and 3 is used to restore NORMAL VIDEO. The alternative is to use INVERSE as part of a program 105 statement. INVERSE is obtained using SYMBOL SHIFT and the M key in E mode. To get inverse video this must be followed by 1, so that to print HELLO in inverse video we key in: 10 PRINT INVERSE 1; "HELLO"' This will appear normally in the program listing, but in inverse when the instruction is carried out. Now add the following lines, and you will see why the use of string variables, and variables for the line and column numbers, can be useful. 70 LET X=X+1 80 LET Y=Y+1 90 CLS 100 GOTO 60 Run the program, and you see we have a crude moving display. CLS makes the screen ‘flash’ a bit, but we could avoid this by overprinting. Revise the program to erase by overprinting empty strings. We can use the graphics characters for pictures. Try this: 10 PRINT AT 0,9; “аша ` _ 20 PRINT AT 1,8; === = 30 PRINT AT 2,8; “ "EE" (it’s supposed to be а car). Change the program to allow you to input a value for Line and Column numbers, so that you can place the car in different places. Then add a GOTO loop to allow multiple cars on the screen. Exercises 1 Write a program that puts: ADDRESS: on the screen, then prompts for inputs on line 20 (INPUT NAME etc), and prints the responses on the screen. Each prompt should overprint the previous one. Allow four separate lines for the address. Blank out the last prompt, then have the screen copied on the printer. 106 Add a routine to LPRINT name, address and age, without the borders or titles, on the printer after deleting the COPY Instruction. Input names, ages and occupations of three friends and arrange them to be tabulated in a suitable form. Experiment with ways to make the car move across the screen. 107 SECTION J: ARITHMETIC AND FUNCTIONS Ji: Arithmetic Operations A prime function of the computer is to evaluate formulae and expressions similar to those used in standard mathematical calculation. Algebraic EXPRESSIONS are written in BASIC using the following OPERATORS with a set of variables or numbers as the OPERANDS. ARITHMETIC OPERATOR EXAMPLE SYMBOL NAME PRIORITY BASIC MATHS in exponentiation 10 А**3 А? (raising to a power) [^1] (on the Spectrum) А13 A? - negation 9 -А -А и multiplication 8 A*B AxB (a.b) / division 8 A/B A+B e + addition 6 A+B A+B _ subtraction 6 А-В А-В Note that negation operates on one operand ~ a unary operation ( i.e. makes a variable negative, e.g. — A) and that the subtraction operator uses two operands, e.g. А-В, a binary operation. J2: Priority 1 All arithmetic, conditional and logical operations are assigned a priority number from 10 to 1. High priority is 10, low priority is 1. The priority numbers for the arithmetic operators are as shown in the previous Unit. 2 The priority of an operation determines the order in which it is evaluated in a complex statement in which more than one operation is to be performed. High priority operations are performed earlier. 3 Brackets (parentheses) are used in BASIC algebraic expressions. Brackets clarify which expressions constitute separate values to be operated on. Expressions inside brackets are evaluated first before the quantity is used in further computation. With multiple (nested) brackets the evaluation proceeds from the innermost bracketed expression to the outermost. 4 For operations of equal priority in the same statement, evaluation is from Left to Right. Brackets can often be omitted when the sequence of evaluation is 108 understood, but there is no harm in using them to ensure correct evaluation. Expressions may be tested by using PRINT as a direct command, to check that you have them correct. For instance key in PRINT (8*2.6/5)*2/3 and press NEWLINE (ENTER). The result will be printed on the screen. If a sequence of direct assignments of values to variables is keyed in first (using LET A = 4 (NEWLINE/ENTER), LET B = 3 (NEWLINE/ENTER), etc.) then variable expressions may be evaluated. Using this facility you should experiment with a variety of expressions until you feel confident that you have understood the way in which expressions are evaluated, and the way you have to formulate an expression in BASIC to ensure it returns the desired result. EXAMPLES 1 Evaluation ofa+b-c In BASIC: A+B-C Operators have equal priority; (1) Left to Right A+B (2) L-*EK (A+B)-C 2 Evaluation of ab , (axb) +c In BASIC A*B/C * has same priority as / H LR A*B (2) L*R (A*B)/C 3 Evaluation of a.(2) ‚ах (b+c) In BASIC A*(B/C) (1) Brackets first (B/C) (2 Multiplication — A*(B/C) But notice we could write the expression without brackets in BASIC as B/C*A This is evaluated: H LR (B/C) (2) L= Е (B/C)*A which gives the correct result. 4 Evaluation of (b° - 6c)*+5 In ZX81 BASIC notation: (B**2 = GG )**24 5 (1) Inside bracket; exponentiation B**2 (2) Inside bracket; multiplication 6*C (3) Inside bracket; subtraction (B**2) - (6*C) 109 (4) (5) Exponentiation ((B**2) - (6*C))**2 Addition (((B**2) – (6*C))**2) +5 In Spectrum BASIC notation: (B 2 - 6*C )#2+5 (1) (2) (3) (4) (9) Inside bracket; exponentiation Bez Inside bracket; 6*C multiplication Inside bracket; subtraction (В%2)-(6“С) Exponentiation (В t 2). – (6*C))4 2 Addition (((B f 2) – (6*С)) # 2) +5 2 Computer evaluation of a.b- © + (e - f) d g In ZX81 BASIC notation: A*B - C**3/D +(E-F)/G (1) brackets E- (2) exponentiation Er (3) multiplication/ division L — R А“В C'"3/D (Е-ЕУС (4) addition/ subtraction L > R (A*B) - (C**3/D) + (Е – Е)/С In Spectrum BASIC notation: А*В - С \ 3/0 +(E-F)/G (1) brackets Е-Е (2) exponentiation OTs (3) multiplication/ division L > R A'B Ct3/D (E-FyG (4) addition/ subtraction L > R (A*B) - (C ^3/D) + (E - FG Evaluation of —70 +2х ^ x3-3x7 In ZX81 BASIC notation: 40 +2 "4702 "3.8." Priority 10 4#**2 16 Priority 9 - 70 Negation Priority 8 2°. te *23 377 LR 96 1 Priority 6 - 70 + 96 — Д1 Result 5 In Spectrum BASIC -70 +2*442*3-3%*7 Priority 10 412 16 110 Priority 9 - 70 Negation Priority 8 2> 15 "TET L — R 96 21 Priority 6 - 70 + 96 - 21 Result 9 Exercises 1 Write the order in which the following BASIC expression 1s evaluated: — А + ((B**3/C) - (A**2/D))*(E + Е)/С (ZX81) — А + ((B 13/C)- (A ^ 2/D))*(E+ F/G (Spectrum) 2 Write down the BASIC expressions for: (i) (и? + 2аѕ)^ (ii) ut + Тағ жа b + ac)" (111) 2a (iv) (xy Work out the order in which each of the expressions is evaluated. Test your results on the computer. J3: Number À positive or negative decimal number whose magnitude is between an approximate minimum of: t3x10 ? and an approximate maximum of: +2 x 10” Zero is included in this range. The smallest number the computer can handle is 2.9387359 x 10 `” The largest is: 1.7014118 x 10° The computer stores and calculates numbers internally to an accuracy of nine or ten digits, but prints out the results of calculations to eight significant figures only, rounding where necessary. J4: The E Notation The E or EXPONENT or scientific notation is the notation computers use for input and output of numbers having a large 111 number of decimal digits. E should be taken to read: ‘times ten to the power of’. For example: 1.73 E5 is 1.73 times 10 to the power of 5 1.73%10%%5 (1.73*10 ^ 5 in Spectrum notation) = 173000. Similarly: 3.8E-7 is 3.8 times 10 to the power of — 7 = 3.8*10** 7 (3.8*10 41 — 7 in Spectrum notation) = .00000038. The computer will accept any number keyed-in in this form and will print out numbers in this notation when their values are outside a certain range. For large positive and negative numbers the E notation is automatically used by the computer for numbers > = 10? Numbers up to this figure are first rounded to 8 significant figures and trailing zeros are added until 107 is reached. Key in and run this program: 10 LET A = 9.9999993E12 20 PRINT A 30 ІЕТА =А + 1Е5 40 СОТО 20 Change line 20 to read: | 20 LPRINT TAB 10;A to get a listing of the result on the printer. For small positive and negative numbers the E notation is automatically used for numbers: <= 10^? To see this in action, key in and run the program below: 10 LET A-1.000001E — 5 20 PRINT A 30 LETA-A -(1E- 12) 40 GOTO 20 Change line 20 to: 20 LPRINT TAB 10;A if you want a printer listing of the changeover. Exercises 1 Key in and run the following simple program, which illustrates how numbers are printed, the E notation and the largest number which may be obtained. 112 10 LETA=1 20 LET A=A*10 30 PRINT A 40 GOTO 20 With the ZX81 press and when the screen becomes full, and the message 5/30 appears on the bottom of the screen to indicate no more room on the screen. The Spectrum will display the ‘scroll?’ prompt. Notice the change to the E notation. Note that the program finally stops itself on the ZX81 with the error message ‘6/20’, which indicates an arithmetic overflow (error code 6) as a result of line 20, i.e. the number is too large for the computer to handle. The Spectrum's response is more precise; the error code in this instance will read: ‘6 Number too big, 20:1’. Change line 10 of the program to each of the following and run the program each time. a) 10 LET A=1.00000000 b) 10 LET A=1.1111111 c) 10 LET A=1.7 d) 10 LET A=1.7014118 e) 10 LET A =1.71 What conclusion do you draw? To show that negative numbers behave in the same way, change line 1@ to the following and run the program. a) 10 LET A= -1 b 10 LET A= -1.7 c) 10 LET A= -1.7014118 d) 10 LET A= -1.71 To show how small numbers are handled by your computer a similar program divides a number (A) by increasing powers of 10. Key in the program and run it. 10 LET A=1 20 LET A=A/10 30 PRINT A 40 GOTO 20 Note the change of notation. Notice that after 1E – 38 the computer prints zeros indefinitely, i.e. it has reached the smallest number it can register. Change line 10 to а) 10 LETA=3 Ы) 10 ІЕТА = 2.9 апа ге-гип the program each time. Notice that 2.9387359 E — 39 is the smallest number before zero. Write this number out in full. Can you think of any applications for very large and very small numbers? 113 6 Change the values of À in the program to negative values and confirm that small negative numbers behave in the same way. PROGRAMS TO SAVE IN YOUR TAPE LIBRARY The following two programs should be keyed in, run, listed and saved for your tape library. They both do what the previous programs did but in addition give a printed copy of the results. 10 REM "LARGE NUMBERS" 20 REM** PROGRAM MULTIPLIES + AND - NUMBERS INPUT FROM THE KEYBOARD BY POWERS O F 10 ** 30 REM **KEY IN VALUES FOR A O P +-1,,4-1.1111111,4-1..7,. + -1.7014118,%- 1.71.** 40 INPUT A 50 LET N=0 60 PRINT А%(10%%у) 70 LPRINT TAB 10;A*(10**N) 80 LET N=N+1 90 GOTO 60 For the Spectrum, replace ** by in lines 60 and 70. 10 REM "SMALL NUMBERS" 28 REM**PROGRAM SHOWS PRINTING OF SMALL NUMBERS** 30 REM**INPUT VALUES OF A AS + -1, +-2.9,+-3.** 40 INPUT A 50 LET N=0 60 PRINT A*(10**N) 70 LPRINT TAB 10;A*(lQ**N) 80 LET М-М-1 99 GOTO 60 J5: Rounding ROUNDING UP The computer will print out computed values to an accuracy of 8 significant figures, ignoring leading zeros. Digits after the 8th significant one will be rounded up. For example, if we key in (as a direct command, followed by NEWLINE/ENTER): 11% PRINT 0.111111111 + 0.888888888 the answer on the screen is 1.Try PRINT 0.0000111111 showing 10 digits can be held exactly. Adding a one on the end forces the use of the E notation. ROUNDING DOWN The INT function returns the nearest integer of the expression X, which is < = X, i.e. it rounds down. e.g. INT 3.9= 3 INT -2.8- -3 INT (4 -8.7 +0.8)= - 4 Try printing these functions. Notice that for negative numbers - 6 is less than - 5, and so on. To round to the nearest integer add 0.5 to the number first: e.g. INT (3.9+0.5) = 4 INT (2.4 + 0.5) 2 ІМТ(-1.7-0.5)- -2 ІМТ(-2.3-0.5)- -2 Notice this assumes that 0.5 rounds (о 1. INT (1.5-0.5) = 2 INT (-1.5+0.5)= -1 Notice we don’t have to enter the zero before the decimal point on the computer (though it doesn’t matter if we do), it’s in that form here for clarity. J6: How Numbers are Handled All computers perform their arithmetic and processing using the BINARY NUMBER SYSTEM In the binary system only two digits are used, 1 and 0. A group of 8 binary digits (bits) is called a BYTE, and we communicate with the computer in Decimal Notation. This is rather more convenient than using Binary. Conversion from Decimal to Binary and vice versa is thus necessary and occurs inside the computer. One BYTE is equivalent to a single character of the computer’s character set. A byte represents a number between 0 апа 255 (decimal). ‘This is why the character codes are in this range (see Section P). A group of 8 zeros and ones can have 2° ( = 256) different states. A digit or number is represented by one or several bytes according to its context in the computer. 115 A character input to the computer or output to the screen or printer is held in one byte. Program line numbers, which are whole numbers 1 to 9999, are held in two bytes. Numbers are held in a form which occupies five bytes. The point to be noted here is that conversion from decimal to binary and back is involved in the operation of the computer, and this conversion is not always exact. This must be allowed for in certain circumstances, especially where the computer is asked to check whether two numbers are equal. A difference in the binary form of the number, however small, will cause the computer to decide they are not equal. In testing two numbers for equality, therefore, if non-integer values have been utilised, and the value of one number arrived at by calculation, the equivalence check should be replaced by assessing the difference. A statement such as: IF ABS(A - В) < 1E-4 THEN... which checks that the difference between the numbers is less than .0001, сап be used instead of IF = B THEN ...., if either A or B has been calculated. The forms in which numbers are held in the computer are considered in detail in Section U — the Computer Memory. J7: Function We define a FUNCTION as Y = F(X) ‘Y equals some function of X, F(X)’ A function is the mathematical relationship between two variables X and Y such that for each value of X there is a unique value of Y. Y takes the function value and is the DEPENDENT VARIABLE. X is the ARGUMENT - the INDEPENDENT VARIABLE. F is the function NAME, e.g. square root, sine, natural logarithm. In a program statement we write, for example: 100 LET Y SOR(X) The argument X can be a single variable, a number or an expression. If X is a single variable or a number it does not need brackets. If it is an expression it requires brackets so that the expression is evaluated before the function is applied to it (so that SOR 9 + 7 gives 10, whilst SOR (9 + 7) gives 4). For example: 100 LET Y = SOR 9 100 LET Y = SOR(B**2—4*A*C) (B42 on the Spectrum) We see that a function is a mathematical operation which gives a number. It is treated in BASIC as a numeric expression, with priority I. 116 The standard mathematical and trigonometric functions are important timesavers for programmers. They are the same as the function keys on scientific calculators. Other functions (utility functions) control or monitor the handling of data by BASIC rather than perform mathematics. If the functions were not available in BASIC we would need to write separate programs to undertake their tasks every time we had need of them! J8: List of Functions used in Sinclair BASIC In this list of functions X is the argument. X is a variable, a number or an expression. If an expression, X must be in brackets. Each of the individual functions will be discussed in more detail later in this section. 1. Standard Mathematical Functions: ABS (X) - gives the absolute value of X EXP (X) - gives e", value of e raised to the power X INT (X) -gives the largest integer < = X, i.e. rounds down LN (X) -gives natural logarithm (value of log. X) SOR (X) -value of V X or X* (X positive) PI -3.14159265 i.e. value of n, PI, which is how it prints on screen SGN (X) -gives sign of X, i.e. whether X is + ve, – ve or Zero. 2. Trigonometric Functions SIN (Х) - value of sine X (X in radians) COS (X) -value of cosine X (X in radians) TAN (X) -value of tangent X (X in radians) ACS (X) -angle in radians whose cosine is X -arccosine Х( - 1 «- X < = 1) ASN (X) -angle in radians whose sine 18 X -arcsine X ( -1 <= X < = 1) АТМ (X) -angle in radians whose tangent is X - arctangent X 3. Special Mathematical Functions RND A random number generating function; gives the next pseudo random number N from a fixed series of random numbers (0 < = N < 1). RAND ( RAND 0) starts the sequence of random numbers in an unknown position. RAND N (ü0 < = N < = 65535) makes RND always return to the same value, if N is the same. 117 4. Character and String Functions CHR$(X) 0<-Х <=255 returns the single character whose code is X. CODE A$ When applied to the string A$, it returns the code of the first character in the string or 0 if the string is empty (null string). LEN A$ Returns the number of characters in the string. VAL A$ Turns a string in number representation into the number for calculation (e.g. A$ = “12.4”, VAL А$ = 12.4). STR$ М Turns the number N into the string “N”. 5. Printing Functions used in the form PRINT F(X) TAB (X) Places the print position in column X. If X>32 then column number is the remainder when X is divided by 32. If it involves back spacing, goes on to next line. Rounds X to nearest integer. AT (X), (Y) Starts printing at line X, column Y бжделлбе21. = Y <= 31 Rounds X and Y to nearest integer. 6. Special Functions INKEY$ No argument. Reads keyboard and senses what key is being pressed at that time. Returns key being pressed as a string, e.g. “А” or ‘‘8’’. If no key is pressed the null string is returned. PEEK X 0 < = X < = 65535 Returns the value of the byte at address X in RAM or ROM memory. USR N Returns the contents of a pair of CPU registers after running a machine code program from address N. N.B. For the Spectrum’s additional functions, see Section W. The above functions, common to both the ZX81 and the Spectrum, are the ones used in the main body of the text. J9: The Function Characters Each of the functions in Sinclair BASIC is represented on the keyboard as a single character word. You don’t have to type the function name letter by letter (if you try to it won’t work), just press the particular function key. Each function character has a special character code and is part of the computer’s character set. Each of the Function 118 characters on the ZX81 is situated at the same position on each key, i.e. bottom outside. To obtain the function the ZX81 must be im FUNCTION MODE, with the F-cursor on the screen. On the Spectrum, all functions are obtained in the Extended mode with the E-cursor on the screen (for further details see Section W1). All FUNCTIONS treated here are in green above the key on the Spectrum, with the exception of ASN, ACS, ATN which are in red below the associated SIN, COS and TAN functions, although they are still obtained in the E-mode. The FUNCTION/EXTENDED MODE only lasts for one function. To obtain successive functions this mode must be repeatedly entered. J10: The Function Character Set Character Code Code (7Х81) (Spectrum) SIN 199 178 COS 200 179 TAN 201 180 INT 207 186 RAND 64 249 STR$ 213 193 CHR$ 214 194 CODE 196 175 PEEK 211 190 TAB 194 173 ASN 202 181 ACS 203 182 ATN 204 183 SGN 209 188 ABS 210 189 SQR 208 187 VAL 197 176 LEN 198 177 USR 212 192 LN 205 184 EXP 206 185 AT 193 172 INKEY$ 65 166 NOT 215 195 п (PI) 66 167 These are the function characters as represented on the ZX81 keyboard. NOT is dealt with in Section R and INKEYS in Section K. Note that ARCSIN, ARCCOS and ARCTAN are used on the ZX81 keyboard but print as ASN, ACS, АТМ, and п prints as РІ. J11: The Standard Mathematical Functions ABS (X) Returns the absolute value or modulus of the value X. X may be a number, variable or expression. ABS(X) gives us the positive value of X. For example: 10 PRINT ABS( - 3.7) gives 3.7 10 PRINT ABS (4) gives 4 Exercises Key in and run this program: 10 INPUT A 20 INPUT B 30 PRINT TAB 3;A; TAB 10;B 40 PRINT TAB 3; ABS (A - B) 30 GOTO 10 Input positive and negative values for A and B. Now change line 40 to: 40 PRINT TAB 3; ABS (A*B) and input some more values. Try replacing the * with ** ( ^ Spectrum), or using ABS (SOR А). N.B. ABS (- 3**3) , or expressions in similar form will not work as the ** ( ^ Spectrum) operator only works for positive first operands. EXP (X) Where X is a number or an expression EXP (X) gives the value of the constant e raised to the power of the value of X e — 2.7183 e.g. 10 PRINT EXP (3.4) i.e. 10 PRINT (2.7183* *3.4) (2.7183 1 3.4 on Spectrum) The function EXP is the inverse to LN. Exercises 1 Using log tables write a program to check the values of e* given in the log tables. 120 2 Write a program which will calculate O from the expression: Q = Qo.e-"* (In BASIC Q = QO* ЕХР(-Т/К“С)) If you know anything about electricity, you might recognise this expression. 3 Key in this program. It calculates a value for e from the formula: e=(1+1/N)**N (^N оп Spectrum) where N is very large. Spectrum users should replace ** by # in lines 30 апа 40. 10 REM “VALUE OF E" 20 ІЕТІ- 1 30 LET N=10**I [^Spectrum] 40 LET E=(1+1/N)**N 50 PRINT TAB 1;N;TAB 12;E 60 LET I=I1+1 70 IF l=5 THEN STOP 80 GOTO 30 LN (X) Gives the value of the natural logarithm. LN (X) = Log, (x) Note that log, (X) (common logarithm) = ( LN(X) )/( LN 10 ) The LN function is the inverse of EXP So: If EXP (X) = Y Then (X) = LN(Y). LN (Y) is the natural logarithm of Y. The antilog is EXP(LN(Y)). The normal log operations can be used if appropriate, as with common logs. For example EXP(LN (X) + LN (Y)) gives the product of X and Y. Exercises 1 10 LEFY=1 20 PRINT TAB 3;Y; TAB 10; ЕХР (LN Y) 30 LET Y=Y+1 40 GOTO 20 Key in and run this program which proves the relationship between the EXP and LN functions. 2 Change 30 to: 30 LET Y = Y*1@ and run again. SQR (X) The function SQR returns the square root of (X), V (X) or Х95, For example: 121 PRINT SQR 9 gives 3 PRINT SQR 23 gives 4.7958315 PRINT SQR (19 + 17) gives 6 PRINT SOR (ABS - 25) gives 5 SGN (X) SGN (X) returns + 1 if (X) is positive, 0 if (X) is zero, — 1 if (X) is negative. SGN is short for Sign or Signum (Signum doesn’t sound like Sine). For example: SGN 23 gives 1 SGN - 5 gives - 1 SGN (3 – 3) gives Q SGN 1 gives 1 SGN (25 - (2*23)) gives — 1 п PI T (which prints on the screen as PI) is a function which has no argument. It returns the value of r as 3.1415927. 3.1415927 is what prints on screen for PI. How would you test whether the computer held any more digits of PI in memory? What happens when you take away 3 from PI? J12: Trigonometric Functions SIN COS TAN The functions SIN (X), COS(X)and TAN(X) give the value of the sine, cosine, and tangent of the number or expression X, which is an angular measure. X must be in RADIANS. We normally express angles in DEGREES. PI = өй. 9... dE. Š 1 DEGREE 180 RADIANS (1 180 radians) To convert degrees to radians multiply by PI/180. For example, if Y is our measure of angle in degrees then: SIN (Y*PI/180) gives the correct value of Sine Y. Exercises 1 Generate a table of values for SIN (X), COS (X) and TAN (X) 122 for every 20 degrees in the range 0 — 360 degrees. 2 Write a program to verify the trigonometric formula: SIN(XX)+COSXX) =1 1+ TAN XX) =SEC*X) 3 Write a program to calculate the area of a triangle from a knowledge of the length of 3 sides and an angle. ACS ASN ATN The functions: ACS (X), ASN (X), ATN (X) give the arc cosine, the arc sine and the arc tangent, respectively, of (X). The returned value is the angle in RADIANS for which the cosine, sine or tangent would be given by the value of (X). To get the angle in degrees multiply by 180/PI e.g. Y = 180/PI*ACS(X) gives arcsin (X) in degrees. Notice these functions print as above, but appear on the ZX81 keyboard as ARCSIN, ARCCOS, ARCTAN. J13: Special Functions Random number generators are useful for games and simulation in statistics. The numbers generated are part of a very long sequence of numbers (there are 65536 of them) and are in fact only ‘pseudo- random’, but good enough for our needs. RND RND gives a random number greater or equal to zero but less than one. 10 LET A = RND assigns a number in the range 0 < = N <1 to the variable A. Notice RND has no argument. If we key in PRINT RND we get a number like .0011251904 or 0.43715682 which is eight or ten digits long and is not much use to anybody in this form. We need to be able to generate random numbers within a useful range, according to our purposes: 1. To obtain a Random Number 0 - 9 To obtain a random number from 0-9 we must multiply our 123 function by 10 and take the integer value. i.e. PRINT INT (RND*10) RND*10 gives random numbers between 0.00000000 and 9.9999999, IN'T( ) will round these values down to integers 0 to 9. 2. Numbers 1-10 Although @ to 9 gives us ten values the range 1 to 10 would be more useful. This is obtained by adding one to the RND function: PRINT INT (RND*10 + 1) Suppose we wanted random numbers generated for simulating a dice roll, we would use: PRINT INT (RND*6 + 1) 3. Random Numbers for a Card Game There are 4 suits, with 13 cards per suit = 52 cards. So if we used: PRINT INT (RND*52 + 1) we could select cards at random. Think about how you could identify the suits and not deal the same card twice. 4. ‘Tossing a Coin There are two outcomes, head or tails, so: 10 LET A= INT(RND"?2 + 1) 20 IF A=1 THEN GOTO 50 aD PRINT “TAILS” 40 GOTO 10 50 PRINT “HEADS” 60 GOTO 10 This program will toss coins until we use BREAK. RAND N RAND is a keyword and is used for controlling the randomness of RND. The computer has a fixed sequence of 65536 jumbled up numbers. RAND N will start RND reading numbers from the Nth number in the sequence. Key in and run this program to prove the above: 10 RAND 7 20 LET Ce=1 30 PRINT RND 40 LET C-C-«1 124 50 IF C<6 THEN GOTO 30 60 GOTO 10 Not amazingly random after all! Exercises 1 Write a program which throws three dice and prints the values thrown across the screen. 2 Write a program to check that the number generated by RND using RAND N is given by RND = (75*(N + 1) - 1/65536). 3 Modify the coin tossing program to count the number of times heads or tails have come up (you need one variable for each). When you've stopped the program by pressing BREAK, you can then access the values by keying in PRINT HEADS, or whatever your variable name is, as a direct command. 4 Write a program to print four groups of three random numbers in the range 1 to 52. 125 SECTION K: STRINGS K1: Strings A string is a set of characters enclosed by quotation marks, e.g. “THIS IS A STRING” or the null string (no characters Typical Strings: “BALL OF STRING" “JANUARY 1ST 1982” “URGHH!” “FAB ** — +/!3” E " (String of spaces) 1234” ore (Null string) Computers handle two kinds of DATA: NUMERIC - numbers ALPHANUMERIC - names or TEXT. The way a computer deals with text is called STRING HANDLING. Strings deal with ALPHANUMERIC information. The sequence of alphanumeric characters is handled in a string as a single unit of data. Characters are defined as LITERALS when placed inside quotes “> They are taken literally to represent themselves. Strings are therefore literals. Characters are IDENTIFIERS where they are not enclosed in quotes. Thus, for example, A represents or identifies a numeric variable and A$ identifies a string variable. Strings can either be of FIXED LENGTH-e.g. always 10 characters long - or VARIABLE LENGTH. The fixed length is determined by the string dimension instruction: DIM A$ (N) where N is the length in characters. Characters which cannot be used in strings A string cannot contain a character that is a line terminator: NEWLINE (ENTER) or TAB. Nor can it contain any of the following: EDIT GRAPHICS RUBOUT (DELETE) FUNCTION BREAK ee (single quotes) 126 All other characters in your computer’s character set can be used. Run the program which checks this: 10 INPUT A$ 20 PRINT A$ 30 GOTO 10 Now try and input some of the above characters. Examples of the sort of text we may want the computer to handle are: — a telephone directory - names and addresses - a timetable - expenses details Computers store all this textual information as strings. String manipulation by the computer would, for our first example, need to deal with: creating the telephone directory sorting the names and numbers into the correct order searching the directory for somebody's number revising the directory, i.e. updating or adding an entry printing out the directory in whole or part. K2: Quotes and Quote Image QUOTES All strings are enclosed in quotes ‘‘’’ when: (1) They are to be INPUT from the keyboard, as in a program line such as: 10 INPUT A$ . When the line is run the cursor оп the screen appears already enclosed in quotes |1 |”. You key in just the characters wanted in the string. (2) When used in programs with the PRINT instruction, e.g. 20 PRINT ‘‘STRING’’. (3) When assigned in a program to a string variable, e.g. 30 LET А$ = * STRING". THE QUOTE IMAGE KEY ON THE ZX81 The QUOTE IMAGE is a special single character on the shift keyboard of the ZX81. 6699 It is used to write ordinary quotes in the middle of a string. eg.10 PRINT "SAY “BELLO” TOO] 127 When the line is run the double quotes will be printed on the screen as single quotes: SAY “HELLO” TOO A special character is needed as two single quotes won’t work. Key in and try to run each of the following lines: 10 PRINT '' SAY “НЕТО”? ТОО” 10. PRINT “БАУ”; "HELLO"; "TOO" 10 PRINT “ SAY "HELLO" TOO" The Spectrum has no QUOTE IMAGE character. Instead, you must put two quotes for every one you want printed. For example, to obtain double quotation marks you type in PRINT“ °>, Single quotes are obtained with PRINT**** ’’’’. Program listings look the same for both machines. K3: String Input On running 10 INPUT A$ the letter cursor appears at the bottom of the screen with quotes round it, prompting you to key in characters for the string = [L] = On the Spectrum this can also be the C-cursor - ‘‘ me STOPPING STRING INPUT When keying in the characters for the string to be input notice that BREAK and STOP have no effect. To escape (1) Use the < key to get outside the quotes. (2) Press STOP, NEWLINE (ENTER) or press | There is a special form of string input, using the INKEYS instruction: INKEYS$ When INKEYS is encountered by the computer it reads the keyboard to determine if a key is being pressed. It does not wait for input like the INPUT instruction. If a key is being pressed it returns the string containing the mode character of the key being pressed. If no key is being pressed it returns the empty string ‘‘’’. 128 The Spectrum returns the mode character with INKEYS$ if in the CAPS mode. We can spend as long as we want before we input a string with the INPUT command, since the cursor will remain on screen. If we want to take advantage of the fact that, unlike INPUT, INKEYS does not require NEWLINE(ENTER) to be pressed, we must arrange a delay. Try this program: 10 PRINT “PRESS A KEY WHEN READY” 20 IF INKEY$-''"" THEN GOTO 20 (no spaces) 30 LET AS-INKEYS$ 40 PRINT “YOU PRESSED ”;А$ Line 20 sends the program back to the beginning of line 20 as long as no key has been pressed. Line 30 makes A$ the single character string returned by INKEY$ when a key is pressed. Due to a design error the Spectrum has far less predictable keyboard scanning using INKEYS than the ZX81. If you type in the program as above on the Spectrum it will work about half of the time. The rest of the time it will skip over line 30. This program will work every time though: 10 PRINT “ PRESS A KEY WHEN READY" 20 PAUSE 0 30 PRINT “YOU PRESSED ”’;INKEY$ Experiment with the two versions to see this problem in action. The action of PAUSE 0 is to stop until a key is pressed. The first key pressed will be the INKEY$. PAUSE will be dealt with later, but remember this quirk of the Spectrum, and this method of dealing with it. The rule is to use PAUSE 0 immediately before INKEYS is used in a program line, to wait for input. Now enter and run this program: 10 PRINT “PRESS 6” 20 IF INKEY$ =“ THEN GOTO 20 (on the Spectrum 20 PAUSE 0) 30 IF INKEY$ = “6” THEN GOTO 60 40 PRINT “FOLLOW INSTRUCTIONS" 50 GOTO 20 60 PRINT “ENDING PROGRAM NOW" 70 STOP Line 20 does the same as before, but line 30 now checks that the right key has been pressed. Notice the 6 must be enclosed in quotes, because INKEYS returns a string. If 6 was pressed, the program goes to line 60. If any other key was pressed, it goes to 40, prints the message, and then is sent back (line 50) to line 20, which waits for another key to be pressed. Games programs, which require interaction, often use INKEY$ in a loop, so that every time the program loops, it checks which key, if any, Is being pressed. 129 K4: Length of a String LEN The length of a specified string A$ is obtained by using the function: LEN A$. The length is given as the number of characters and is the current length of the string. Spaces are included in the length of a string. EXAMPLES 1 10 LET A$=‘‘SINCLAIR”’ 20 PRINT LEN A$ Check that the result is 8. 2 10 LET AS= “А B’’ (9 spaces between A and B) 20 PRINT A$ 30 PRINT LEN A$ Key in and run. 3 10 LET A$- “PRINT” 20 PRINT A$ 30 PRINT LEN A$ Key in the program first with PRINT formed from separate keys, and then change line 10 so that PRINT is formed by pressing the key. Why are the answers different? 4 10 INPUT A$ 20 PRINT A$, LEN A$ 30 GOTO 10 K5: Null Strings A string with no characters is called a null string. For example: LET A$ — 6699 The length of the string is 0. A string which contains spaces is not a null string. A space is a character obtained by pressing [SPACE] . The null string is returned by INKEYS if no key is being pressed. Exercises 1 Key in and run the following program: 10 ТЕГА" 130 20 PRINT A$ 30 PRINT LEN A$ 2 Key in and run this program: іё LET A$e!' ” 20 PRINT A$ 30 PRINT LEN A$ К6: String and String Array Variables AS is a string variable used to store strings. It consists of a single letter (À to Z), followed by the dollar sign. Twenty-six variables of this type are thus possible. The Spectrum accepts upper and lower case letters, but treats, e.g. k$ as the same string as K$. AS(N) is a string array variable or string list variable where N refers to the number of strings in the list. String lists must be dimensioned as an array before the string array variable can be used, by the DIM (DIMension) instruction. Using the array notation, an unlimited number of string variables are possible. Again, the Spectrum accepts upper and lower case letters, but does not differentiate, e.g. b$(N) and B$(N) are the same. Caution: A$(N) can have two meanings in a program. (1) It can refer to the N’th character in a string A$. (2) It can refer to the N'th string in a list or array of strings. In this case the string array must previously have been dimensioned with a DIM A$(N) instruction. K7: String and String Array Dimension STRING DIMENSION DIM AS(N) sets a fixed length of N characters for the string. For example: 10 DIM А$(6) sets a length of 6 characters for the string А8. 131 If strings of length <N (less than N characters) are assigned or input, then space characters are added to make up the complete string of length N. Spaces do not show up on the screen when they are printed! (To check they are in the string we can ask for their character set code to be printed using the CODE instruction. We'll get to this later.) If more characters than the number allowed in the DIM AS$(N) statement are assigned from INPUT or LET statements they are ignored. If strings are not dimensioned their length is effectively unlimited. The DIM statement fixes the length of a string until changed by another DIM statement. LEN is thus not useful when strings are dimensioned. STRING ARRAY DIMENSION The DIM statement for string arrays has the form: DIM A$ (N,L) where N = number of strings and L = the fixed length of each string. A may be any single letter A to Z, but must NOT be the same as a simple string variable. Each string is set to contain L spaces initially. For example, DIM A$(3,4) will reserve storage space for 3 strings, A$(1), A$(2), A$(3), each of length 4, іп the string array A$. K8: String and String Array Assignment STRING ASSIGNMENT Strings are assigned to string variables using the LET or INPUT instructions. For example: LET A$ = “А STRING" or INPUT A$ This establishes a value for the string. As we shall see later, the value may be a literal value in quotation marks, or a string or substring value. STRING ARRAY ASSIGNMENT 5 DIM А$(3,9) 10 LET AS(1)- “SINCLAIR” 20 LET А%(2)- ‘‘COMPUTING’’ 30 LET А$(3) = *COURSE" assigns 3 strings to the string array variable А$(3). 132 We can also use an INPUT instruction: 10 INPUT А%(1) 20 INPUT A$(2) 30 INPUT А$(3) Exercises 1 Key in and run this program: 10 DIM A$(2,9) 20 LET A$(1)- “PERSONAL” 30 LET A$(2) = 'COMPUTING " 40 PRINT А$(1), A$(2) 2 Now key in and run this. Input different strings of varying length. The string length is set at 8 in line 10. 10 DIM AS$(3,8) 20 INPUT AS(1) 30 INPUT А$(2) 40 INPUT А$(3) 50 PRINT А%(1) 60 PRINT А%(2) 70 PRINT А$(3) 3 Key in and run this program: 10 DIM AS(6) 20 INPUT A$ 30 PRINT AS$ 40 PRINT LEN A$ 50 PRINT АФ “ЕМГ” 60 GOTO 20 line 10 sets a length of 6 characters for A$ line 20 asks you to input a string line 30 prints the string line 40 prints the size of the string in terms of characters line 50 prints END starting directly after the 6th character in the string line 60 loops us back to input another string a) INPUT less than 6 characters. See that the remaining characters are spaces. Notice that LEN A$ always gives 6 even though different numbers of characters are input for А8. b) INPUT 8 characters. Notice the extra characters are ignored. K9: Substrings and String Slices A SUBSTRING or a STRING SLICE is any set of consecutive characters taken in sequence from the parent string. For 133 example, for the string – “ABCDEFG'”: a substring 15 “СПЕЕ” or “АВС” or шм Ы А substring сап Бе а single character. SPECIFYING SUBSTRINGS AS(P TO Q) «ANYSTRING" (P TO Q) where P is the first character and Q the last character of the substring wanted іп the strings A$ or ‘‘ANYSTRING’’. SUBSTRING ASSIGNMENT Any substring is itself a string. We can assign a string to a substring: 10 DIM А$(12) 20 LET A$ (1 TO 4) = “JOHN” 30 LET A$ (6 TO 10)- *SMITH" 40 PRINT A$ This program assigns strings to substring variables. EXAMPLES 1 2 3 10 PRINT “SINGLAIR” (2 TO 5) prints INCL 10 РКІМТ “SINCLAIR” ( ТО 3) prints SIN, since 1 15 assumed if it 1s omitted at the start. 10 PRINT “SINCLAIR” (3 TO ) prints NCLAIR (omitting the character after TO means the last character in the string 15 assumed). 10 PRINT ‘‘SINCLAIR” (3 TO 3) prints М. This is more conveniently written as 10 PRINT “SINCLAIR”” (3) Or 10 LET A$- ‘‘SINCLAIR”’ 20 PRINT А$(3) which prints the 3rd character in A$, exactly as with a literal string. | 10 PRINT “SINCLAIR” (1 ТО 0) prints 4” 1.е. gives the null string (по characters). Here is a program that uses names and numbers in single strings: 134 10 LET А%-"МАМЕ AGE" 20 LET BS="TOM 16" 30 LET C$z"BILL 14% 40 LET D$=" JANE 17" 20 PFINT АТ 1567;AS$C1 TO 4); АТ 1:14:8%(6 TO 8) £20 PRINT АТ 4.,&:E$C1 TO 4); AT 4; 14:Е%с(6 TO 7) 70 PRINT АТ 7s6*C$(1 TO 4); AT 7%:14:С%(6 TO 7) SO FRINT АТ 1016; D$(1 TO 4); АТ 10:14:1%(6 TO 7) Notice how we spread the print out using substrings. K16: String Concatenation A$ + B$ Concatenation means chaining strings together. It is derived from the word catenary meaning a chain. What the computer does is to ‘add’ them together to form a new string. “СОМ” + “PU” + “TER” = “COMPUTER” 10 LET A$ = “СОМ” 90 LET B$ = “PU” 30 LET C$ = “TER” 40 LET T$ = A$ + B$ + C$ 50 PRINT T$ Note that the + operator is used for string concatenation. We cannot subtract, multiply, divide strings or raise them to powers, because they are not numbers. Although the ‘adding’ of concatenation uses the same symbol it is not an arithmetic operation. Key in and run the example program given above. Add some DIM statements to the program: 2 DIM А%(6) 4 DIM В5(6) 6 DIM C$(6) Run it. You will notice that although the strings are chained they are far apart. Why is this? Now try this program: 10 INPUT А5 20 INPUT BS 30 PRINT А5,В5,А5%В65 40 LET AS = А54В5 50 PRINT А5 60 LET А$=А$+А$ 70 PRINT А5 Notice іп line 40 уге have incremented the string Бу adding B$ оп to A$. This gives us a new A$ made up of the old A$ plus B$. The statement in line 60 is equivalent, in string terms, to having a line which for numeric variables says LET A= A+A. K11: Comparing Strings The conditional operators: = <> <= < >= > may be used between strings and string variables using the IF... THEN instructions. For example: IF A$ = “YES” THEN GOTO .... IF N$ = B$ THEN PRINT .... IF A$< = B$ THEN GOTO .... When the computer compares strings of characters it does so by comparing the codes of each of the characters in sequence. A string is found to be less than another if it comes first in alphabetic order. If the strings contain numbers we should remember that numeric codes are less than alphabetic (letter) codes. This affects comparisons. (See Section P for the character codes.) Strings are compared in order of characters from left to right. For example: “AS, ЗЫ” "AD S A “А”< “АА” a d.e d “АЗ S “А4” “б” "LE = A “4Д” Key їп and run the next program. Input the strings above plus others you want to try and it will print out their relative alphabetic orders. 10 INPUT A$ 20 INPUT BS 30 IF А5<В5 THEN GOTO 70 40 IF А5-В5 THEN GOTO 99 50 PRINT А5;">";В5 60 5ТОР 70 PRINT A$;"«"; BS 80 STOP 90 PRINT A$;"-";B$ 100 5ТОР 136 This gives us a method for putting names into alphabetic order, like in a telephone directory. We also have a method of searching it, since we can check whether any name in the list is equal to the desired name. We have already used string equality, but here’s another example of string comparison: 10 PRINT "DO YOU UNDERSTAND STRINGS?" 20 PRINT “ANSWER YES OR NO" 30 INPUT А5 40 IF AS = "YES" ТНЕМ GO ТО 70 50 PRINT “THEN READ THE SECTION AGAIN!" 60 STOP 70 PRINT "YOU ARE A GENIUS!" 88 STOP Key it in and run it. Do you understand? The above assumes the use of capital (upper case) letters only on the Spectrum. For lower case letters, these are all after upper case letters in the ordering of strings. So on the Spectrum: AA<Aa Z<a Z1<z1 SMITH<Smith So any ordering of strings must take this into account. For this text we assume the use of capitals throughout. Exercises 1 The “TELEPHONE” program sets up a telephone directory with names and telephone numbers. It will search through its lists to find the telephone number corresponding to a given name. Run and analyse the program to find out how it works. 10 REM "TELEPHONE" 20 REM **PROGRAM SETS UP A TEL EPHONE DIRECTORY AND USES IT** 30 PRINT "HOW MANY NAMES DO YO U WISH TO ENTER INTO THE DIRECTO Ry?" 40 INPUT N 50 PRINT 60 PRINT “INPUT ";N;" NAME (20 LETTERS) AND NUMBER(8 FIGS) PAIR 5" 70 DIM А$ (М, 20) 80 DIM BS(N,8) 90 DIM DŠ (20) 100 PRINT 137 110 PRINT 120 PRINT "NAME";TAB (22); "МОМВ ER" 130 PRINT 140 FOR F-1 TO N 150 INPUT А$Ѕ (Е) 160 PRINT AS(F); 170 INPUT BS(F) 180 PRINT TAB (22);BS$(F) 199 NEXT F 200 PRINT 210 PRINT 220 PRINT "TO CLEAR THE SCREEN TO USE THE DIRECTORY PRESS CONT AND NEW LINE KEYS" 230 STOP 240 CLS 250 PRINT 260 PRINT "WHAT NAME?" 270 INPUT D$ 280 REM **NEXT PART OF THE PROG RAM SEARCHES FOR THE NAME** 290 PRINT 300 PRINT D$; 310 FOR F=1 TO N 320 IF AS(F)-DS$ THEN GOTO 370 330 NEXT F 340 PRINT 350 PRINT "NAME NOT FOUND" 360 GOTO 260 370 PRINT TAB (22);BS(F) 380 PRINT 399 PRINT 400 PRINT "ANOTHER МАМЕ? (Y/N)" 410 INPUT QS$ 420 IF Q$-"Y" THEN GOTO 249 430 PRINT 440 PRINT "TO KEEP YOUR DIRECTOR Y AFTER SAVING, USE ""GOTO 240"" WHEN RUNNING THE LOADED PROGRAM қ NOT ""RUN""," 450 PRINT 460 PRINT "BYE FOR NOW" 470 STOP 2 Modify “ТЕГЕРНОМЕ” to create your own directory with your friends’ names and addresses or birthdays or telephone numbers. a) Redesign the program b) Document it c) Key it in d) SAVE it e) Debug it D LLIST it g) SAVE the working version h) Put it in your personal tape library 1) Enter details in your notebook 138 K12: Strings and Numbers In addition to the handling of strings as strings, there are instructions which enable us to convert strings to numbers, numbers to strings, and to usefully manipulate various numerical values of strings and their characters. We have already dealt with LEN. The other available string functions are dealt with here. The first two instructions cover the character set which is dealt with in Section P. CODE A$ When applied to a string A$ CODE returns the character set code number of the first character in a string. For example: 10 LET X = CODE “MOTHER” On the ZX81 X becomes 50, the code for M (CODE “М”). When applied to a single character substring, it returns the code of the substring: e.g. 10 LET A$ = “CODE” 20 PRINT CODE А$(3) prints 41, the CODE for D (CODE ‘‘D’’). The Spectrum uses a different code to the ZX81 (called ASCII, an international standard). Thus, CODE “MOTHER” is 77, and CODE А$(3) in the above is 68 (= CODE ‘‘D’’). CODE A$ (M,N) When applied to a string array CODE returns the character code of the N’th character in the M’th string. For example: 10 DIM A$(10,10) 20 LET A$(1)- ‘‘SINCLAIR’’ 30 LET А$(2) = “BASIC” 40 PRINT CODE A$(2,3) will print 38 (CODE‘‘S’’) on the ZX81, whilst on the Spectrum the *S' in ASCII code is 83 (there is no significance in one being the reverse of the other!). CODE А$(2), applied to a string array as above, would return the CODE of the first character in A$(2), just as when applied to a literal string or string variable. 139 CHR$ When applied to a number М, CHR$ N gives the single character string in the computer’s character set whose code is the number N. For example, on the ZX81: CHR$ 49 15 “L” CHRS 12 is “£” whilst on the Spectrum CODE ‘‘L”’ is 76 and CODE *'£" is 96, so CHR$ 76 gives “1.” on the Spectrum, and CHR$ 96 gives **£^', We can treat these characters as elements in a string and make up a word by concatenation. Try this on the ZX81: 10 LET A$=CHR$ 63 + CHR$ 61 + CHR$ 36 + CHR$ 29 20 PRINT A$ or this on the Spectrum: 10 LET A$=CHR$ 83 + CHR$ 80 + CHR$ 69 + CHR$ 67 +CHR$ 84 + CHR$ 82+ CHR$ 85 + CHR$ 77 20 PRINT A$ VAL A$ Applying VAL to a string containing only numeric characters and arithmetic or logic operators, returns the result of the arithmetic inside the string. For example: 10 PRINT VAL ‘14+2+3”’ prints 6 10 LET A$= 43” 90 LET BS =**4” 30 PRINT VAL (A$ + B$) prints 7 All recognised arithmetic functions can be used: 10 PRINT VALSSOR 16" (prints 4) 10 PRINT VAL “ABS -29” (prints 29) An interesting use of VAL is where alphabetic and numeric information in a string can be treated as substrings. Arithmetic can 140 then be performed on the numeric substring. For example, try this program which gives the total ages of three people in a group. LET ñ$="SMITH 23" LET ES="JONES 24" LET C$z"WEZT 17" LET T= VAL A$ca TO 93+ VAL BELS TO 935 VAL СФЕ TO 99 PRINT AS РЕІМТ E$ PEINT C$ PRINT з» “TOTAL AGE "FT; "^ YEARS“ STR$ STR$ (N) returns the value of (N), a numeric expression, as a string. For example: STR$ 3.4 gives “3.47 STRS$ (3*31) gives “93” STR$ (SOR 4) gives ‘‘2”’ STR$ is the complementary or opposite function to VAL To see STR$ in operation, and the complementary functions of VAL and STR$, try this program: 10 20 Exercises LET X23 LET Ү=0. 5 LET А%= ZTR$ (X/Y) FEINT A$, VAL AS (ЕТ BS=AG+ 5ТК% X PRINT E$, VAL ES/2 LET t= VAL С STRE С VAL AS+ VAL ЕФ)? PRINT С 1 Write a program which inputs a number of strings calculates the total number of characters in each, and the total number of characters in all the strings. 2 Write a program which calculates the total price of items in a shopping list, after receiving and printing out the string inputs of each item and its cost. and 3 Write a program which will print a calendar for any month of next year. Key in the month names and lengths as a string in the program. 141 SECTION L: LOOPS L1: Loops A loop is a block of instructions that the computer executes repeatedly until a terminating condition is met. The usefulness of loops can be seen by considering three forms of a program to print out the first one hundred positive integers. 10 PRINT 1 20 PRINT 2 30 PRINT 3 9 Ww $ 6 P» ce te @ S 1000 PRINT 100 This program, which does not use a loop, is 100 statements long. This next program uses a conditional jump loop which does the same thing and uses only five statements. 10 LET C=90 20 LET C-C-«1 30 PRINT C 40 IF C< 100 THEN GOTO 20 90 STOP The third program uses a FOR - NEXT loop which is the commonest method of looping in BASIC, and the most economical in program lines. 10 FOR F - 1 TO 100 20 PRINT F 30 NEXT F 40 STOP All loops have four characteristics: 1 Initialisation (start value of counter) 2 BODY of loop 3 Modification oí counter 4 Exit condition. Loop structures may be properly formed in two ways: 1 CONDITIONAL GOTO STATEMENT LOOPS 2 БОҚ... NEXT LOOPS Loops are extremely useful. They allow repeated procedures to be performed, and the values of the counters, which are modified each time the program passes through the body of the loop, may also be used in calculations, if care is taken. 142 L2: Counters Here are two examples of the use of the conditional GOTO loop: 19 LET C=0 ZO LET Себа 30 FRINT "COUNTING" 40 IF C “= 10 THEN GOTO 20 90 PRINT "FINISH" 10 LET С=0 20 LET CsC*1 20 INFUT A 40 FRINT А ФО IF Cz10 THEN GOTO 20 60 PRINT “END OF NUMBERS" The variable C is used as a counter in these programs, adding 1 every time the program loops. 7f the value of C is less than the value set then the GOTO statement is executed and the program loops. If it is greater then control passes to the next program line. This enables us to control the number of times the program lines within the loop are executed. Our procedure for using counters in the example programs above is: 1 Initialise the counter 2 Increment the counter (add 1) 3 Do the task 4 Check the counter. If it has not reached the final value then go back to item 2. If it has then program exits from the loop. Note that we can perform the incrementation of the counter in a different place: 1 Initialise 2 Do the task 3 Increment counter 4 Check the counter. If less than specified value, GOTO 2. If more than specified value, program exits from the loop. We must be careful to set the conditions properly to achieve our desired result (the correct number of passes through the loop). Look at the first two simple programs above again. How many times will each of them pass through the body of the loop? Which is wrong if we wanted to loop exactly ten times? If you don’t see the answer, key them in and run them. The GOTO statement in the program below enables the program to loop continuously between lines 50 and 80. This would continue indefinitely so it is important to get out of the loop at the appropriate point. This is achieved by line 60 utilising the IF (condition) THEN GOTO (line-number) statement. Notice that the value of the counter (N) 1s used inside the loop: 143 „Ө REM "SIMPLEI" 20 PRINT “SEVEN TIMES TABLE" ЗО PRINT “UP TQ TIMES 20" 40 LET N=0 20 LET N=N+1 &O IF М>20 THEN GOTO 100 70 PRINT N+ 7#N so GOTO 50 100 REM **#ЕМП++# Notice that the counting procedure in this program is set up differently again. Line 50 increments the counter. Line 60 checks the counter value. In this case, the IF- THEN statement has the effect of transferring control out of the loop if the counter exceeds 20, with the GOTO 100 statement. The procedure in this case is: 1 Initialise 2 Increment 3 Check counter. If greater than specified value, jump to program end. 4 Body of loop 5 Return to 2. Key in the program. Run it to check it loops exactly twenty times. Then EDIT line 60, to insert: 75 IF N> 20 THEN GOTO 100 and delete line 60. Now run it. It is surprisingly easy to miss the desired number of loops, if you are not careful with the structure of the loop, and the exit conditions. (Change N220 in line 75 to N> = 20 and the program will loop the correct number of times). Different procedures using counters give different program structures. Look at the flowcharts of different counter procedures. Remember that the conditional test can put to use the >, <, >=,<=, = operators, as appropriate. 144 COUNTER FLOWCHARTS Counter = Start Value Counter = Counter + Step of loop Exit Loop 145 Yes Counter = Ətart Value Body of Loop Counter = Counter + Step Counter = Finish Value No Exercise Consider a simple program to work out the squares of the first 20 integers. 19 PRINT "NUMBER", "SQUARE" 20 LET М-й 30 LET N=N+1 40 IF N»20 THEN GOTO 70 50 PRINT N,N*N 60 GOTO 30 70 REM*END OF PROGRAM* 146 The GOTO statement in line 60 will cause the program to loop continuously between lines 30 and 60. This would continue indefinitely but line 40 is inserted so that the program jumps out of the loop when N>20. N is used as a counter. Line 20 initialises N and line 30 increments N by 1 each time the program goes round the loop. Write a program which calculates and prints the square and the cube power of even numbers between 10 and 30. The counter will need to be incremented by 2 each time the loop is executed by a GOTO statement. Write a program which loops 10 times (counter 1 to 10) but uses another counter to print the squares of the ten numbers 5.25, 5.0, 4.75 са. 3.0. L3: For – Next Loops This is a more convenient way of having a program loop. The loop is set up with the FOR... TO ... STEP and NEXT instructions used in combination. The loop goes from the first value to the last value, counting by adding the defined STEP value every time it loops until the exit condition is met. FOR (variable) = (first value) TO (last value) STEP (step) FOR C = (N) TO (M) STEP (X) where C is the counter variable or control variable of the loop and (N), (M) and (X) are numeric expressions. C can be any single letter À to Z. It must not be the same as a single letter numeric variable. It is initialised at value (N). (N), (M) and (X) may take any values, positive or negative, as long as repeated additions of (X) to (N) will reach (M). If STEP is omitted, + 1 is assumed. NEXT C indicates last line of the loop. It adds (X) to C and loops back if the total is less than (M). The program loops back to the line after the line with the FOR - TO - STEP instruction. The FOR - NEXT loop has a fixed procedure, unlike loops formed with conditional GOTO instructions. We form a FOR - NEXT loop in a program like this: 10 FOR F - 0 TO 100 STEP 2 rue: Body of loop 40 NEXT F The FOR statement initialises the loop. 0 is the start value 100 is the stop value F is the counter variable and is initialised as Q STEP 2 is the increment. 147 NEXT F is the last line of the loop and increments the counter F by the STEP value. We can also decrement the counter (decrease it). For example: 10 FOR F=100 TO 0 STEP -2 (where the decrement is 2) The loop will be exited in the first example when Е>100 and in the second when F«0. F will take values 0, 2, 4 .... 98, 100 in the first case, and 100, 98 .... 4, 2, 0 in the second. Any program lines in the body of the loop will be repeated each time the program loops. Try these simple examples: 10 FOR F=2 TO 4 STEP 1.3 20 PRINT F 30 NEXT F 10 FOR F=4 TO -1 STEP -1 20 PRINT F 30 NEXT F 10 FOR F=-2 TO 4 STEP 2 20 PRINT F 30 NEXT F 40 PRINT 50 PRINT "F EQUALS ";F;" ON EXIT" Convince yourself that this doesn’t work: 10 FOR F-2 TO 4 STEP - 1 20 PRINT F 39 NEXT F The next one is an interesting example of the inaccuracies in the computer’s arithmetic: 10 FOR Е-1.2 TO -0.3 STEP - 0.2 20 PRINT F 30 NEXTF The only reason for using F as the control variable is that it is convenient: FOR F can be entered just by pressing the F key twice. You can use any letter, but it is good personal programming practice to use the same letters consistently, and not use these for single letter variables. ‘I’ is often used by programmers as a control variable (I for Integer) but can be confused in program listings. This next example uses N: 10 FORN=1TO15STEP 1 20 PRINT N,N*N 30 NEXT N We can use the value of the control variable in calculation within the loop. Edit STEP 1, so that line 10 reads: 107 FOR N= 1 TO 13 and run it again. STEP may only be omitted for a STEP of + 1. 148 In the program, line 10 allows N to go from 1 to 15 with a step value of 1. That is to say, N takes the values, 1, 2, 3, 4, 5, 6, 6, 8, 9, 10, 11, 12, 13, 14, 15 each time performing the calculations within the loop. The next program illustrates the use of different values for the step. The value can be positive or negative, integer or non-integer. In the case of decimal increments or decrements there is the possibility of rounding errors if the loop is executed many times — it is therefore advisable to use integer values for the step and divide by the appropriate power of ten, if the loop variable is to be used in calculations. If this were done in the program below, lines 130 and 140 would read: 130 FOR N^ 10 TO 56 STEP 7 140 PRINT N/10; TAB 8; (N/10)**2; TAB 16; (N/10)**3 ( ^ on Spectrum) The program calculates squares and cubes for: a. a Seer, > 31 (line 20) 129, 115, МӘ, „аже 60 (line 70) L, Leds X tone wwe жж 5.6 (line 130) Once again, Spectrum owners should remember that their machine uses the ‘up-arrow’ ( 4) rather than the ZX81’s stars (**) to represent ‘to the power of’. 5 REM "MULTILOOP" 10 PRINT "NUMBER"; TAB 8; "SQ UARE"; TAB 16; "CUBE" 20 FOR N-1 TO 31 STEP 3 30 PRINT N; TAB 8; N**2; TAB 1 6; N**3 40 NEXT М 45 PRINT "ТҮРЕ СОМТ KEY" 50 STOP 60 PRINT "NUMBER"; TAB 8; "SQU ARE"; TAB 16; "CUBE" 70 FOR N=120 ТО 60 STEP -5 80 PRINT N; TAB 8; N**2; TAB 1 6; N**3 90 NEXT М 100 PRINT "ТҮРЕ СОМТ KEY" 110 5ТОР 120 PRINT "NUMBER"; TAB 8; "SQU ARE"; TAB 16; "CUBE" 130 FOR N=1 ТО 5.6 STEP .7 140 PRINT N; TAB 8; N**2; TAB 1 6; N**3 150 NEXT N In this next program the total is represented by T which is initialised equal to zero (line 10). Each time the program goes through the loop the INPUT number is added to T (line 40) so that when the loop (lines 20 to 50) is exited T represents the sum of the ten numbers input. The 149 program evaluates the average by dividing the total by the number of numbers input. 5 REM “АУЕКАСЕ” 10 LET T=0 20 FOR N=1 TO 10 30 INPUT X 40 LET T=T+xX 50 NEXT N 60 PRINT “AVERAGE =”; 7/10 This program illustrates a loop used to print a table. In this case a heading is given (line 70) and this must be outside the loop as it is only required at the beginning. We require all names and ages to be tabulated so the print statement doing this (lines 140, 150) must be within the loop. Finally, we require the average age, which is to be printed underneath, and so the print statement (lines 170, 180) is inserted after the loop has been completed. 10 REM "LOOPS3" 20 PRINT "THIS PROGRAM PRINTS OUT THE NAME AND AGE OF A GROUP OF PEOPLE AND WORKS OUT THE AVERAGE AGE" 30 PRINT 40 PRINT "INPUT NUMBER IN GROU 5Ø INPUT X 60 LET T= 70 LPRINT "NAME", "АСЕ" 80 FOR N=1 TO X 99 PRINT "INPUT NAME" 100 INPUT N$ 110 PRINT “INPUT AGE" 120 INPUT A 130 LET T=T+A 140 PRINT N$,A 150 LPRINT N$,A 160 NEXT N 170 PRINT "AVERAGE AGE-"; T/X;" YEARS" 180 LPRINT "AVERAGE AGE"; T/X;" YEARS" The flowchart of a FOR - NEXT loop would be drawn like this, if we used the standard set of symbols as presented in the unit on programming: 150 BODY OF LOOP No Yes EXIT So for a program like the following: 10 FOR F= 2Т0%5ТЕР.5 20 PRINT F*F 30 NEXT F 40 PRINT “ЕМГ” the flowchart would be like this: 151 However, FOR - NEXT loops are used so frequently that this is a somewhat inefficient way of representing a loop of this type. ‘There is another symbol often used, although it is not a standard symbol, which condenses all the required information. This has the form: 152 OUT OF LOOP END LOOP TO BODY OF LOOP Our example program would be represented like this: L4: Loops of Variable Length The first value, final value and step of a loop may have any values (including variables which may be specified using INPUT). The first example shows a simple program which allows all conditions in the FOR statement to be specified using the INPUT statement. 153 REM "VARLOOP" PRINT "ТҮРЕ INITIAL VALUE" INPUT I PRINT "ТҮРЕ FINAL VALUE" INPUT F PRINT "ТҮРЕ STEP" INPUT S PRINT "X","X**244*X-3" [ ^ Spectrum] FOR N=I TO F STEP 5 LET YsN**244*N-3 [ 4 Spectrum] PRINT N,Y NEXT N It is important in such calculations to avoid the case where 'division by zero' occurs. À simple shown below: example of how this may be done (line 40) is REM "DIVZER" PRINT "X","1/(X-3)" PRINT FOR N=-9 TO 15 STEP 3 IF М-3-0 THEN GOTO 80 LET Y-1/(N-3) PRINT N,Y GOTO 90 PRINT N,"INFINITY" NEXT N The final program in this section illustrates another way of having a variable loop size. The operator may use this program for any number of numbers between 1 and 100. A marker (in this case — 1) is set to indicate when the input is complete, allowing a Jump out of the loop (line 69). This is a ‘dummy value’ — a value not normally entered. (N.B. DO NOT JUMP INTO THE MIDDLE OF A LOOP i.e. a loop must always be entered from the FOR statement.) REM "STDDEV" LET T-0 LET 5-й LET С-й PRINT "THIS PROGRAM WORKS O UT AVERAGE AND STANDARD DEV IATION OF A SET OF NUMBERS" PRINT PRINT "TYPE NUMBERS ONE AT A TIME,TO FINISH TYPE -1" FOR N-1 TO 100 INPUT X IF X--1 THEN GOTO 140 LET T=I+X [ ^ Spectrum] LET S=S+X**2 LET С=С+1 NEXT N PRINT PRINT "AVERAGE IS ";T/C PRINT "STANDARD DEVIATION I S ";SQR (S/C-(T/C) **2) [ 4 Spectrum] 154 The procedure used in this program can confuse the flow of a program and must be used with care. It is useful on occasion, but it is preferable to have only one entry and one exit from a loop. In this program, the loop may be exited from line 90 in addition to the normal termination, when №100. L5: Nested Loops We can place one loop inside another loop, so that every time the program goes through the outside loop, it will perform the inner loop sequence. The inner loop must be entirely within the outer loop. Loops are said to be NESTED one inside the other. Loops can be nested to any depth, i.e. we can have as many loops as we wish, as long as they’re correctly arranged. 30 FOR A=1 TO 6 40 FOR B=1 TO 3 in hs ТТТ Inner Loop | Outer Loop 80 NEXT B | 120 NEXT A To have a third loop correctly placed, it would have to be inside the B (Inner) Loop, or outside the A (Outer) Loop. Be careful to avoid crossing the loops: 10 FOR A=1 TO 6 20 FOR B=1 TO 3 80 NEXT B Programs with wrongly arranged loops will run, without giving an error message, but won't give you the correct answers! To illustrate the use of nested loops, here are two programs. The first evaluates and prints out the squares, cubes and fourth powers of the first ten integers. Each number (N = 1 TO 10) is to be raised to the appropriate power (E=1 TO 4). Note that the loops are correctly nested. 20 FOR N=1 TO 10 Ee FOR E- 1 TO 4 50 NEXTE REM "NEST" PRINT "NUMBER";TAB 7; "SQUAR E";TAB 14; "CUBE";TAB 21;"4T H POWER" 20 FOR N=1 TO 10 30 FOR E-1 TO 4 40 PRINT TAB (E-1)*7;N**E; [^ Spectrum] 50 NEXT E 60 PRINT 70 NEXT N н Qu You will get a printout that starts off like this: NUMBER SQUARE CUBE 4TH POWER 1 1 1 1 2 4 8 16 3 9 27 81 4 16 64 256 The flowchart for the ‘‘NEST1’’ program, using the flowchart symbol for FOR - NEXT loops we have introduced, will look like this: START We can see the sequence of operations by tracing the program. Line 20: Line 30: Line 40: Line 50: Line 60: Line 70: This table uses the ZX81 symbol for exponentiation. Notice how line 40 uses the value of E to format the output. The second example assumes that a company employs three salesmen who keep sales figures for each week. At the end of four weeks the company requires a summary of sales to be printed. Each salesman S (1 TO 3) has weekly takings W (1 TO 4). Notice again that the loops are nested within each other. 30 FOR S=1 TO 3 gon 70 FOR W=1 ТО 4 110 NEXT W 130 NEXT S NAME WEEKi WEEK? WEEK3 WEEK4 JONES 12 16 19 13 BROWN 23 26 29 21 SMITH 31 4 6 39 10 REM *NEZTED* 20 LPRINT "NAME": ТАБ 6: "МЕЕК1 TAB i2:;"WEEKZ": TAB 207 "WEEKS ТАЕ 27: "WEEK4" ЗО FOR 5-1 TO 3 40 PRINT “INFUT SALESMANS NAME - - - - че ча >30 INFUT N$ EO ІРКІМТ N$; 79 FOR W=1 TO 4 SO PRINT "TYPE WEEK "М" SALE 90 INPLIT X 100 LPRINT TAB (7*W-1);X 110 NEXT W 120 LPRINT 130 NEXT $ 157 Exercises Write programs using loops to perform the operations stated: 1 Calculate the reciprocals (1/N), logarithms (LN N) and cubes (L**3 ог L 4 3) of even numbers between 20 and 36 and print them out in a table. An object is dropped and the variation of distance s with time t is given by s=4.9t*. Print a table of the distances fallen for each second from 1 to 15 seconds. Evaluate and print the values of ЗХ? + 4X — 7 for values of X between 6 and 8 in steps of 0.25. Evaluate SIN X for values of X from 0? to 360? in intervals of 10°. Remember you must convert from degrees to radians. Print out the results in two columns. Print a table of the discount at 5%, 10%, 15%, 20% on articles from £100 to £200 in steps of £10. Find the sum of all odd numbers between 39 and 75. Find the sum of the series 1,1,2,3,5,8,... (Fibonacci) to 20 terms. (Each term is the sum of the previous two terms.) Find all numbers less than 50 which can be written as the sum of two squares. (e.g. 13 = 2° + 3°) A ball is dropped from a height of twenty metres and rebounds one-half the height on each bounce. What is the total distance it travels? Assume the ball stops bouncing on its hundredth bounce. 158 SECTION M: PLOTTING M1: Plot and Unplot The screen size is the same on both the ZX81 and the Spectrum. It is divided into 24 x 32 character cells in the same way for printing on the screen. The bottom two lines are reserved for use by the computer. However, the plot screens of the ZX81 and Spectrum differ. The principle is the same, that of dividing up the screen into small squares, each of which can be blacked in separately, but the Spectrum has a higher resolution plot screen than the ZX81. This means that the screen is divided up into smaller squares (called pixels, short for picture elements) on the Spectrum. The Spectrum has extra graphics commands not available on the ZX81 which make use of these pixels, some of which are mentioned in this Unit, but are dealt with fully in Section W. The commands are also different on the two machines, so we will describe the two separately before dealing with some of the uses of these commands. Spectrum users should note the principles of plotting as presented here (even where we note that a particular process is easier using one of the Spectrum graphics commands, since it is the principles that are important, and can be extended to more complex tasks), and not just feel superior to the ZX81 user, who has no access to CIRCLE or DRAW! On both machines each pixel is specified by X,Y co-ordinates. Thus, on the ZX81 (0,0) is the bottom left-hand corner and (63,43) is the top right-hand corner. There are 4 pixels in each character cell. PLOT X,Y - blacks out the picture element (pixel) with co- ordinates X,Y. UNPLOT X,Y - blanks out the pixel with co-ordinates X,Y. The PLOT co-ordinates run from 0 to 63 across the screen left to right (X co-ordinates) and from 0 to 43 up the screen bottom to top (Y co-ordinates). As a memory aid, remember that X is ‘a cross’, and X before Y. It is a simple matter to print horizontal and vertical lines. This program plots a horizontal line across the screen: 19 FOR N = 0 TO 63 20 PLOT N,20 30 NEXT N See if you can write a program that plots a rectangle. Each of the character cells on the Spectrum’s screen has 8 x 8 = 64 pixels, and there are thus 176 in any column up the screen and 256 in any line across the screen. Once again specifying each pixel with X and Y co-ordinates, 0,0 is the bottom left-hand corner and 255,175 is the top right-hand corner. Whilst PLOT X,Y on the Spectrum blacks in the pixel element in 159 exactly the same way as on the ZX81, there is no UNPLOT statement on the Spectrum. To erase the dot again the OVER 1 facility is used. Thus, to erase at X,Y you must enter a multiple statement line. OVER 1: PLOT X,Y - blanks out the pixel at co-ordinates X, Y Although it is perfectly possible to plot a horizontal line to the screen using a program similar to that used on the ZX81: 10 FOR N=8 TO 255 20 PLOT N,20 30 NEXT N it is far simpler on the Spectrum to use the following type of formulation: 10 PLOT 0,20: DRAW 255,0 It is also possible to get some semblance of motion. ‘The program below moves a dot across the screen: On the 2Х81 On the Spectrum 10 FOR N= 0 TO 63 10 FOR. N= 0 TO 255 20 UNPLOT N - 2,20 20 PLOT OVER 1; N - 2,20 30 PLOT N,20 30 PLOT N,20 40 NEXT N 40 NEXT N It 1s possible to construct simple shapes using PLOT. Here is a ZX81 routine to draw a (somewhat stylised) dog: 10 LET X=0 20 LET Y=10 38 PLOT X,Y 40 PLOT X+1,Y-1 50 FOR N=2 TO 4 68 PLOT X+2,Y-N 70 NEXT N 80 PLOT X+3,Y-2 990 PLOT X+4,Y-2 100 FOR N=1 TO 4 110 PLOT X+5,Y-N 120 NEXT N 138 PLOT X*6,Y 140 PLOT X+7,Y-1 It can sometimes be worth remembering that the PLOT pixels are not exactly square. The visible variation from square will depend on the type of plotting being done, and the particular TV screen in use. It is worth drawing what should be a square on the screen, and simply measuring the variation with a ruler. Try running this program, and do this for different areas on the screen, so that you can check if the variation is constant. Note the double loop, which is often useful in PLOT routines. On the ZX81 On the Spectrum 10 FORF-10 TO 30 10 FOR F=10TO 100 20 FOR L= 10 TO 30 20 FOR L=10 TO 100 30 PLOT F,L 30 PLOT F,L 40 NEXT L 40 NEXT L 50 NEXT F 50 NEXT F 160 The variation from square on the screen is typically in a ratio between 1.1:1 and 1.2:1 (across screen/down screen). This means a ‘square’ that looks square will need to be 10 pixels across and either 11 or 12 pixels down. Most PLOTting is done utilising loops. To PLOT a circle we need to choose a suitable STEP value for a loop that runs either from @ to 360 (degrees), or 9 to 2 PI (Radians). We also have to set a centre to give us a circle where we want it, and a radius such that it will fit the screen. For a circle in degrees, code in this program: On the ZX61 On the Spectrum 10 FORD=0TO360STEP10 10 FOR D=0 TO 360 STEP 2 20 LET R=D*PI/180 20 LET R=D*PI/180 30 LET X=30+20* COSR 30 LET X=120+80* COS R 40 LET Y=20+20* SINR 40 LET Y=80+80* SINR 50 PLOT AY 50 PLOT X,Y 60 NEXT D 60 NEXT D Line 2@ converts to radians, in which all the trigonometric functions of the computer work. Line 30 calculates the horizontal component, and line 40 the vertical. The SIN and COS functions are multiplied by 20 (80 оп the Spectrum) to give a radius of 20 pixels. The centre is set for the 7Х81 at pixel 30, 20, and for the Spectrum at pixel 120, 80. In most cases, it is convenient to consider the PLOT screen to be 60 x 40 pixels (ZX81), rather than 64 x 44, in order to set scales and position plots оп the screen, and 240 x 160 similarly for the Spectrum. Having set the basic values, we can introduce variations within the loop into the above program. We can calculate the radius value and get a spiral plot. Alter the program to: For the ZX81 For the Spectrum 10 FORD-20 ТО 360 STEP10 10 FORD-0 TO 360 STEP 2 20 LET Z = D*PI/180 20 LET Z= D'PI/180 30 LET R-Z*3 30 LET R-Z*10 40 LET X = 30 + R*COS Z 4) LET X = 120 + R*COS Z 5) LET Y=20+R*SIN Z 30 LET Y=80+R*SIN Z 60 PLOT X,Y 68, PLOT Q<, Y 70 NEXT D 70 NEXT D Calculating additional values, all within the loop, and using the loop values as a basis, provides complex shapes fairly easily. Alter the first three lines of the program: For the ZX81 For the Spectrum 10 FOR D = 0 TO 360 STEP 5 10 FOR D-0 TO 360 20 LET Z=D*PI/180 20 LET Z=D*PI/180 30 LET R= 20*SIN(Z*4) 30 LET R =60*SIN(Z*4) RUN it. From a simple circle, we now have the basis for a polar graph plot and can identify a scale of values for PLOTting that will fit the screen. Similarly using parametric equations for the ellipse on the ZX81, X goes from 10 to 50 as COS goes from - 1 to 1 and Y from 10 161 to 30 as SIN goes from — 1 to 1 round the circle. Notice this uses radians directly (2*PI radians = 360 degrees). Spectrum plot points are multiplied by 4. For the ZX81 10 FOR N-0 TO 2*PI STEP PI/20 20 PLOT 30 + 20*COS N, 20 + 10* SIN N 30 NEXT N For the Spectrum 10 FOR N =0 TO 2*PI STEP PI/180 20 PLOT 120 + 80 *COS N, 80 + 40*SIN N 30 NEXT N Try altering the multiplication factors in line 20 for different ellipses. Alter the STEP value to get a continuous line. Of course, on the Spectrum a simple CIRCLE statement enables us to achieve the same result demonstrated in our first example much more quickly. For instance: CIRCLE 128,88,50 will draw a circle of radius 50 pixels with its centre in the middle of the screen. This is included with the additional Spectrum functions in Section W. Note however that the calculated circles are more accurate than the ones drawn using CIRCLE, but a lot slower to PLOT! Exercises 1 PLOT the extreme corner pixels, measure the rectangle and use the computer in command mode to calculate the proportions of a pixel rectangle on your screen. 2 PLOT a circle, using radians directly, without a degree conversion, with another circle, half the radius, inside. 3 PLOT a more accurate circle with allowance made for the pixels being non-square, by altering the multiplication factors for either COS or SIN. 4 Change the spiral routine to produce a double spiral (i.e. going round the circle twice). 5 Experiment with the rosette producing program. Alter the values of R in line 30 by changing the factor by which Z is multiplied. Try Z**2 (Z^42 on Spectrum) and similar expressions. M2: Graph Plotting Simple graphs may be plotted using the PRINT functions already encountered. The following program illustrates its use for drawing a histogram. Lines 20 to 70 allow twelve values to be input and make Z the largest value input. Lines 90 to 150 plot out the histogram allowing the maximum value (i.e. Z) to be 25 columns long and all the others are drawn in proportion. 162 10 REM "HISTO" 20 DIM M(12) 30 LET 2-0 40 FOR N=1 TO 12 50 INPUT M(N) 60 IF M(N) > 2 THEN LET Z=M(N) 70 NEXT N 80 REM **PLOT** 90 FOR N-1 TO 12 100 PRINT N;TAB 4; 110 FOR L-1 TO M(N) STEP 2/25 120 PRINT "*"; 130 NEXT L 140 PRINT 150 NEXT N Result: LKR KKK ke e e e ke e e ke e e e e e Х 2 **k* d kk ke ke e ke e e e e e 4 kkKKKKKEK 5 ЖЖЖЖ Ж б á kkkkkkkkkkkkkkkkkkkkkkkk 7 ж 0 kkkKKKKKKKK О KkKKKKKK 10 ****#****@**@**%*m*@**w**w** 11 ****x* 12 *********@**@*w* The STEP value in the program above is a SCALE FACTOR. The use of a suitable scale factor is needed in most graphical routines. Here is another version of a barchart program that identifies the scale factor and uses it to multiply the values to be plotted out using the asterisks. (The graphics characters can be put to use to draw solid bars, where the asterisk is used here.) 10 REM *BARCHART* 20 PRINT "ENTER MAX VALUE" 30 INPUT M 40 LET SCALE-25/M 50 PRINT "ENTER VALUES (MAX 2 0) ENTER -1 TO FINISH" 60 PAUSE 150 70 CLS 80 FOR F-1 TO 20 90 PRINT AT 21,0; "INPUT VALUE ";F 100 INPUT V 110 IF V--1 THEN Goro 190 120 PRINT AT F,0; V 130 PRINT AT F,5; 140 LET V-V*SCALE 150 FOR T-1 TO INT (V4.5) 160 PRINT "*"; 178 NEXT T 180 NEXT F 190 PRINT AT 21,0;" " 163 The identification of scale factors to produce the best plot possible within the avallable X,Y values on the screen is vital in all plotting routines. The plotted functions have to be plotted on the biggest scale that will enable them to fit the screen. This program fits the screen without any problem: ZX61 10 FOR X =0 ТО 60 20 PLOT X,SQRX 30 NEXT X Spectrum owners should bear in mind that each pixel you can PLOT on the Spectrum is a quarter as wide and a quarter as high as those on the ZX81. Thus, as a general rule, you should allow for a factor of four when working with ZX81 scales, as shown in this discussion of scaling factors. In the program above, for example, the first line would read FOR X =0 TO 246. The program above does not give the best illustration of the shape of the curve, although it has the X,Y scales the same (one pixel = 1). Changing line 20 to: 20 PLOT Х;2“5ОКХ gives a better graph. It is obvious, in this instance, that we could increase the scale factor — in this case the number by which we multiply SOR X to get the Y value —to 5, and the graph would still fit the screen. But if we try this program (do!): ZX61 Spectrum 10 FOR X =0 TO 60 10 FOR X-0 TO 240 20 PLOT X, X*X 20 PLOT X,X*X 30 NEXT X 30 NEXT X we would only get a few points plotted before the computer stops with an ‘integer out of range’ error code. It is obvious that the maximum value in this case will be 60 x 60 = 3600 (7Х81) and 240 x 240 = 57600 on the Spectrum. So if we used: 20 PLOT X, X*X/100 20 PLOT X, X*X/400 the highest value for the Y pixel would be 36 on the ZX81, which makes use of most of the screen. (For the Spectrum it would be 144.) In most cases, however, it 1s not so easy to see what the scale factors should be. We have a 44x64 screen to use on the ZX81 and а 256 x 176 screen on the Spectrum, and so in general, for positive values only, suitable scale factors are given by: ZX81 Spectrum (X axis) 65 259 Largest value of X Largest value of X (Y axis) 43 175 Largest value for Y 164 Largest value for Y For a full range plot of a function that takes positive and negative values, for example SIN, we have to set a scale factor which refers to the screen available for use above and below the pixel Y value taken as zero. To give an example, for a SIN function, taking values between +1 and -1 we set the zero line as Y=20 (7Х81) or Y = 80 (Spectrum). We then need to find a scale value such that the Y values vary between 20 above and 20 below this line (80 above and below for Spectrum) as SIN varies between + 1 and - 1. Again, it is obvious that we need to use a line like: 2Х81 Spectrum 20 PLOT X, 20 + 20*SIN X 20 PLOT X, 80 + 80*SIN X To get a single full range curve we need X to vary from 0 to 2PI radians, so we can use: 10 FOR X -0 TO 2*PI STEP 2*PI/60 20 PLOT X, 20 + 20 *SIN X [80 + 80 *SIN X on Spectrum] 3 NEXT X for full screen use. (Remember 2PI radius = 360°.) Up to now, although you have been told about the co-ordinates of the PRINT and PLOT screens, we have treated the use of PRINT and PLOT as two separate areas. Since the PRINT and PLOT co-ordinate systems refer to the same screen, the two may also be used in concert, but care must be taken. Confusion is likely to arise between the numbering systems, not so much in the numbering across the screen, but in the Y plane, where pixels count 0-43 (@-175 оп the Spectrum) upwards, and the print lines 0-21 downwards. Pixels are coded X,Y, across and up, print positions L,C, down and across. The screen grids for printing and plotting are reproduced here for both the ZX81 and Spectrum. 165 THE ZX81 PRINT AND PLOT SCREEN You cannot PRINT or PLOT on the bottom two lines. «—— Lines An example: this is Columns —— the pixel (57,32) 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 x 48 | 50 | 52 Pixel x-coordinates PHT Pixel y-coordinates ----ь 166 An example: this is the pixel чыш | = E = О Q ESI q — s3}2uIp1009 Á |axid 6/1. ¿9L 861 161 ЕРІ SEL 721 GLL Lit EOL 96 ZB 62 14 БӨ SS Zh ФЕ IE EE Gt и 891 091 ZSL vti 961 821 001 Zit VOL 96 88 08 22 v9 95 BH OF ZE vC 9 8 0 38 еу ~ <+ š бәш| OM} uuolloq eu) uo | 1014 10 LNIHd Aijeuuou 1ouueo под N33439S 10 ld '? Іміна WNYLOAdS JHL Pixel x coordinates ——— р> It is useful, when both PRINTing and PLOTting on the screen, to work with one screen grid first, and then add the other grid. As an example, consider graph titles. We could, to get a title for a printout of a graph, use a direct command: PRINT ‘‘GRAPH OF Y = X**2/100’’, then use COPY, BREAK the COPY routine after the first lines printed, then PLOT the graph with our program and COPY that, but it’s not very elegant. We want the title on the screen with the plotted graph. We can first set the PLOT routine, for example: ZX61 Spectrum 10 FOR N=0 TO 60 10 FOR N-0 TO 250 20 PLOT N, N*N/100 20 PLOT N, N*N/400 30 NEXT N 30 NEXT N By inspection, after RUNning the routine, we can add a title where it will not interfere with the PLOT. 40, PRINT AT 0, 35: “27 50 PRINT AT 1,0; “Y =X 7100 This gives us a screen with everything on it, with the bonus of using standard notation for X°, not the BASIC’s ** (fon Spectrum) notation. A different function might require the PRINTed strings to be placed elsewhere. Exercise Write a program that will calculate the pixel co-ordinates of any PRINT square (character cell). Input L and C (for Line and Column), with suitable prompts erased by an empty string, and output “Piel” s Х; 4)”; Ү; 16 top right’’, etc. For the ZX81, output the four pixels in any specified character cell. For the Spectrum, output the X,Y co-ordinates of the four corner pixels. 168 SECTION N: SUBROUTINES N1: Subroutines A subroutine im BASIC is a program module performing an allotted task and is entered using a GOSUB statement. The section of program Is completed and exited by a RETURN statement which sends the computer back to the line following the GOSUB statement. A subroutine must only be entered via a GOSUB statement and exited by a RETURN statement. Two instructions are used to create subroutines. GOSUB (line number) - transfers control to the specified line number RETURN —leaves subroutine and returns control to the line immediately after the GOSUB instruction which transferred control to the subroutine. Spectrum users have probably noted that their machine prints GO SUB with a space. Here is an example of the program structure for these instructions: IBS ,.. 110 GOSUB 500 --------(1) Таб ... TO uw 140 GOTO 600 520 REM *SUBROUTINE* (3) 5318 vs 520 ... dy (4) 539 wns 540 RETURN 600 STOP (1) GOSUB - goes immediately to line indicated (500) (2) Continues program (lines 500-540) until RETURN reached (3) Program returns to line 120 (line immediately after GOSUB statement). (4) Itis vital to ensure that a subroutine is not entered accidentally when writing the program. Note that line 140 does this by using a GOTO statement to bypass the subroutine. Line 600 may continue the program, or be a statement such as REM*END OF PROGRAM”. It is a useful practice to end a program at the highest line number, which indicates successful completion of the whole program. The alternative, stopping the program with a line 140 STOP, could also be used. 169 Subroutines are often used for repeated procedures and may be thought of as separate program structures: MAIN ROUTINE SUBROUTINE 100 114 GOSUB 500—~>|500 REM SUBROUTINE * 120 -&——— 510 130 520 14) GOSUB 500— 1530 REM * END OF SUBROUTINE * 150 =< 540 RETURN 160 The computer stores the line number of the GOSUB instruction (whereas it doesn’t with a GOTO). The RETURN instruction transfers control back to the line number after the /atest GOSUB. As shown above, this means we can enter a subroutine repeatedly in the course of a program. N2: Subroutine Example The example program given below evaluates the circumference and area of a circle, and has a subroutine to round the results to two decimal places. The program works as follows: (1) Calculates the circumference (line 40), and makes this figure equal to variable Z (line 45), which is the variable the subroutine will round. (п) Enters subroutine (line 50). (ш) Corrects answer to 2 significant figures (subroutine lines 200 — 230), and returns with rounded value of Z to line 60, which: (iv) Prints out circumference (line 60). The same procedure is then repeated for the area, the subroutine being entered (called) again in line 90. Lines 200 to 23@ of the program are then executed again, but the RETURN statement this time returns control to line 100 (the next line after the last GOSUB statement). It is essential to have line 110, which prevents the subroutine being entered accidentally when the calculation is complete. 10 REM "CIRCLE" 20 PRINT "TYPE RADIUS" 30 INPUT R 40 LET C=2*PI*R 45 LET Z=C 50 GOSUB 200 60 PRINT "CIRCUMFERENCE IS ";2 70 LET A=PI*R**2 [ ^ Spectrum] 80 LET Z=A 90 GOSUB 200 170 100 PRINT "AREA IS ";Z 110 GOTO 3609 120 REM *MUST NOT ENTER A SUBROUTINE EXCEPT BY A GOSUB* 200 REM **SUBROUTINE TO CORRECT TO TWO DECIMAL PLACES** 210 LET Z=INT (100*(Z4.005)) 220 LET Z=Z/100 230 RETURN 240 **END OF SUBROUTINE** 300 REM **END OF PROGRAM** The second example is a program to evaluate the sum of the series 1 4 1/2! +1/3! +.. 41/10! to 6 decimal places. (The exclamation mark (!) means ‘factorial’. Factorial 5 (5!) is 5x 4x 3x2x 1, etc.). In this program there are two separate subroutines. The subroutines are both entered repeatedly. The first is to evaluate the factorial and the second corrects the answer to 6 decimal places. Although it is not essential to use subroutines in such a program it does improve the structure and make it considerably easier to follow the sequence of operations. 19 REM "FACTORS" 40 LET 5-й 50 FOR 2-1 TO 10 60 GOSUB 200 70 LET T=1/X 99 LET S=S+T 100 PRINT Z;" TH TERM IS ";T 118 NEXT Z 120 GOSUB 300 130 PRINT 140 PRINT "SUM OF SERIES ";V 150 GOTO 400 200 REM **SUBROUTINE FACTORIAL** 210 LET X=1 220 FOR N=1 'TO Z 230 LET X=X*N 240 NEXT N 250 RETURN 300 REM **SUBROUTINE 6 D.P. ** 310 LET V=INT (1E6*(S+5E-7) ) 320 LET V-V*1E-6 338 RETURN 400 REM **END** Results on screen: TH TERM IS 1 ҮН TERM IS 0.5 TH TERM IS @.16666667 TH TERM IS .041666666 TH TERM IS .083333333 ; - 0013888889 TH TERM IS .0001964127 TH TERM IS .000024801587 TH TERM IS 2. 7557319Е-6 TH TERM IS 2.7557319E-7 SUM OF SERIES 1.7182862 = оо - OY Ut i» Q N = < = "3 г = = ні о - 171 Trace the program through for the first two terms to ensure that you can follow the flow. N3: Nested Subroutines This technique is similar to nested loops in that a subroutine is entered from another subroutine. In the simple example given the program enters the first subroutine (line 300) and from within this calls up the second subroutine (line 320 calls up subroutine at line 400) which is completed and returns (line 420) to the first subroutine which is then completed. See the diagram below of the program flow. Hand trace this program to discover the result of running it. (N.B. This program is only used to illustrate nested subroutines and the calculation carried out clearly can be done more easily without their use. ) 10 REM “SUBROUTINE1" 20 LET M=5 30 GOSUB 300 40 PRINT M 58 GOTO 569 300 REM ****1ST SUBROUTINE**** 310 LET М=М+1 320 GOSUB 400 330 REM **RETURN TO MAIN PROGRAM** 340 RETURN 350 REM * k k k oo k k # k k k k k k k k k k k k Kk 400 REM ****2ND SUBROUTINE**** 410 LET M=M* (M+1) **2 [ # Spectrum] ‘20 RETURN 430 REM k k k k k k k k k k k k k k k k k k k k k k k 500 PRINT "END OF PROGRAM" The diagram illustrates the procedure in the above program for two nested subroutines. 30 GOSUB 300 40 50 сото 500 (7) 360 33$ sans 320 GOSUB 400 oo peas 34@ RETURN Е" (3) 35D .... (5) 49D .... 410 .... 420 RETURN 430 owes (1) Subroutine 1 is called at line 30. Enter first subroutine at line 300. (2) Start executing first subroutine. (3) Subroutine 2 is called at line 320. Enter second subroutine at line 400. (4) Execute second subroutine. (5) RETURN at line 420 returns program to line 330 (line following GOSUB call). (6) Continue execution of first subroutine. (7) | RETURN at line 340 returns program to line 40 (line following GOSUB call). (8) Statement to avoid entering subroutines accidentally. The second example is typical of a computer games program. The nested subroutine ensures that the computer’s move is printed out each time before the player makes his move. 10 REM "NESTSUB" 20 REM **PART OF GAMES PROG** 30 LET х-3 40 GOSUB 600 45 PRINT 50 PRINT "YOUR MOVE WAS ";M 60 PRINT "COMPUTERS MOVE ";X 70 STOP 600 REM **SUBROUTINE PLAYER** 610 GOSUB 700 620 PRINT "YOUR MOVE?" 630 INPUT M 640 RETURN 700 REM **SUBROUTINE COMPUTER** 710 PRINT "COMPUTERS MOVE ";X 720 RETURN Note that it would make no difference if the nested (called from a subroutine) subroutine were to start at a lower line number than the subroutine which called it. Subroutines are always discrete program modules, wherever they are located in a program. N4: Recursive Subroutines A recursive subroutine is a subroutine that calls itself. This facility 1s not available in some versions of BASIC used on other computers. For some purposes this can be a very useful program structure. From within a subroutine, a GOSUB instruction is used to transfer control so that the program re-enters the subroutine. The computer stores each GOSUB call, with the line number to RETURN to, just as if the GOSUB call had been made to a different subroutine. The RETURN instructions are executed in reverse sequence to the order in which the GOSUB instructions were encountered. The example program below evaluates the factorial. of any number N, input as an integer less than 30. First the program, then the explanation: 173 20 КЕМ 20 PRINT 30 INPUT М "RECSUE" "TYPE NUMBER<20" 40 IF М>20 THEN GOTO 200 S50 БОЦЕ 100 80 PRINT F 20 КЕМ 20 REM жЕ € € 93€ зен 3€ 9€ ж 1 THEN GOTO 140 100 REM *#+##SUBROLUT INE ++ 110 IF N <> 120 LET F=1 iso GOTO 180 140 LET NzN-1 150 GOZE 100 160 LET F=F*(N+1) 170 LET N=N+1 120 RETURN 135 REM **##*# END SUE жж 190 КЕМ 200 РЕІМТ “OBEY INSTRUCTIONS, РЕ ESS RUN AND NEWLINE/ENTER" 210 КЕМ **END#* To help us decipher the program flow, we can insert PRINT statements and add a counter, in order to code the GOSUB and RETURN instructions with a number to indicate the sequence in which the recursive calls are performed. Add the following lines to the program: 5 LET C=90 35 PRINT N 45 LET C=C+1 55 PRINT “RETURN TO MAIN РКОСКАМ” 145 LET C=C+1 146 PRINT “GOSUB CALL ”;С 147 PRINT “N=";N 155 PRINT''RETURN CALL “G 156 LET C=C-1 165 175 PRINT “Е=”;Е PRINT “N =’’:N (sets counter to count GOSUPB calls) (prints first value of N) (first GOSUB call from main program) (final RETURN executed) (increments counter each time GOSUB is used recursively) (prints each time GOSUB is used recursively) (value of N before each recursive GOSUB call) (prints each RETURN call as made, corresponding to the GOSUPB call of the same number) (decrements counter as each RETURN is executed) (value of F at each stage) (value of N at each stage) Then run the program for N = 3. The resulting ‘machine trace’ screen display 1s: 174 3 GOSUB CALL 2 N=2 GOSUB CALL 3 N=1 RETURN CALL 3 F=2 N=2 RETURN CALL 2 F=6 N23 RETURN TO MAIN PROGRAM 6 If we draw up a trace using the data from this display (as below), we will see that the GOSUB at line 150 is executed for each value of N from 1 to N. The RETURN calls are then made for each value from 1 to N, calculating F each time (line 160) and incrementing N (line 170), so that the value of factorial N is calculated as 1x2x3...x N. The flowchart of this program is quite simple, but the algorithm is not clear unless the sequence of GOSUB and RETURN calls is understood. The computer stores each GOSUB call in sequence in a portion of memory called the GOSUB stack, and each RETURN instruction removes one of these stored GOSUBSs, passing control to the line after the GOSUB call. Confusion is possible with recursive subroutines because the RETURNS are made to the same program line each time (line 160 in this case). “RECSUB”’ - Trace јот N = 3: 50 GOSUB(1) 60 100 N-3 N=? N=1 110 F 120 130 140 Nš2 Nš! 150 GOSUB(2) GOSUB(3) 160 E 170 180 R F = 1*9 F v 2%3 N=2 N =3 TURN(3) RETURN(2) RETURN(1) - (To main program) 175 Flowchart - ‘‘RECSUB”’ START ©) (2) F=F*(N+1) RETURNS TO LINE RETURN AFTER LAST GOSUB CALL. В) 176 Notice that line 130 passes control to the RETURN statement of line 180. Check for yourself that line 130 could be a RETURN instruction and the program would still run correctly. This is likely to result in a less visible flow in the program, however. The next program has a subroutine (starting at line 100) which calls itself in line 150. As for the previous program, insert suitable PRINT statements to print out the values of the variables and the number of GOSUB calls made. Hand trace the program for suitable integers, e.g. 15 and 25. The program evaluates the highest common factor of the two numbers input. Note that in this case there are no processing statements between the GOSUB call in line 150 and the RETURN instruction of line 160. The sequence of RETURNS will be executed by control going repeatedly to line 16@ (the line after the GOSUB call), which does the next RETURN, until the last stored GOSUB is encountered, which will pass control back to line 5@ of the main program. 5 REM “HCF" 10 PRINT “TYPE ‘TWO POSITIVE INTEGERS" 20 INPUT M 30 INPUT N 49 GOSUB 100 50 PRINT "ANSWER IS";P 68 GOTO 220 100 REM **SUBROUTINE** 110 LET P=N 120 LET N-M-N*INT (м/м) 130 LET M=P 140 IF М-й THEN GOTO 160 158 GOSUB 100 210 REM 220 REM **gND** N5: Computed Gosubs The line number N in a GOSUB N program instruction may be a computed expression: it is permissible to have any expression as the numeric value for a line number. We can make use of this in programs where we want to give the user some options of operations. Since we would write the program with these options as subroutines, a suitable choice of line numbers can allow us to present a menu to the user. Here are two (useless) examples to illustrate the principle: 1) 10 PRINT "MAIN PROGRAM" 20 PRINT "INPUT 1 OR 2" 30 INPUT X 40 GOSUB Х%100 50 PRINT "MAIN PROGRAM ENDS" 69 PRINT "NOW BACK TO MENU" 70 PRINT 80 GOTO 10 177 100 PRINT "FIRST SUBROUTINE" 110 RETURN 200 PRINT “SECOND SUBROUTINE" 210 RETURN 2) 10 REM *NESTED SUBS FOR MENU** 20 REM **INITIALISE MENU GOSUB** 30 LET MENU-14009 40 REM **MAIN PROGRAM** 50 PRINT "MAIN PROGRAM" 60 REM .... 70 PRINT "NOW TO MENU" 80 PRINT 90 GOSUB MENU 100 PRINT "MORE MAIN PROGRAM" 118 PRINT "MENU OR END PROGRAM?" 120 PRINT "INPUT M OR E" 130 INPUT NŠ 140 IF N$-2"M" THEN GOSUB MENU 150 GOTO 9999 1000 PRINT TAB 3;"MENU" 1010 PRINT ,,"1. OPTION 1",,"2. OPTION 2" 1020 PRINT "INPUT 1 OR 2" 1030 INPUT M 1040 GOSUB (M*1000)+100Q 1050 RETURN 1100 REM ****SUB l*****x* 1110 ВЕМ k k k k k k k k k k k k k * k 1120 PRINT "SUB 1 COMPLETED" 1130 PRINT 1140 RETURN 2100 REM ****SUB 2****** 2110 REM £ k k k k k k k k k k k k k k 2120 PRINT "SUB 2 COMPLETED" 2130 PRINT 2140 RETURN 9999 STOP Notice the use of a variable ("MENU") to hold the line number (1000) of the Menu subroutine (Lines 20 and 30). This technique can be useful as a mnemonic in longer programs, and can help the user identify which program module has been called. This technique can be combined with the use of INKEY$ to give an instantaneous jump to the required subroutine. The program waits for a key to be pressed and then jumps to the required subroutine. 10 PRINT "PRESS 1 FOR SUB 1"," PRESS 2 FOR SUB 2" 20 IF INKEYS="" 30 LET AS=INKEYS THEN GOTO 20 35 IF А5-"1" OR А5-"2" THEN СО TO 60 40 PRINT "KEYS 1 OR 2 ONLY PLE ASE" 50 GOTO 10 60 GOSUB VAL А5%100 70 PRINT "BACK TO MENU" 80 GOTO 18 178 PRINT "********k*kkkkkk" PRINT "SUBROUTINE ONE" PRINT "*********X**x" RETURN PRINT "soo x de e e e e x n PRINT "SUBROUTINE TWO" PRINT "s***k*kkkxkkx" RETURN Spectrum users should replace line 20 with 20 PAUSE Q N6: Subroutine Use: Example As an example of the use of subroutines, here is a guess-the-number game. The program has three subroutines, one to get the number (lines 150 — 190), one to check the guess (lines 210 — 300), and one for the success message (lines 350 — 410), which sets the marker MARK to tell the main program, which is the loop between lines 50 and 140, whether the number N (computer's number) is the same as G (the player's guess). This defines whether the success subroutine has been called as a result of the conditional test in line 110. 22 10 20 30 REM "GUESSNUM" LET MARK =0 LET TRIES=0 PRINT “GUESS MY NUMBER, "++, “NUMBER: IS BETWEEN 1 AND 99" (M9 е „ ts cC uy < ord -— — ЫҢ М. !. Же _ — “ІЛ -- ұл pe bh FS p I 63 3 Кә ка 0 CY oo ез» йу, — 1 — i+ p» pee de dex ooo C on oO ch <s C) ! о ) LE" TR КЕМ жж СЕТ NUMBES жж ces LIE FO ES=TRIE'S+1 PRINT ss “ENTER YOUR GUESS" INFLT Ж oe” Ramee ane ӘЕМ жж GOSIP CHEE ж DOSJE ооо REM жж GOSUB SuUmTE Ss жж IF DIFFzO THEN SOSE 280 REM x CHECK MARK жж IF MARK=! THEN GOTO Soo БЕМ x LOOP BACK жж GOTO So ES cA каға REM XX%3 3333333333 3333 XE CE REM ** БЕТ NUMBER SUE: жж MEM 333 3 3 09 Ж € 0€ 303€ 9€ EHH LET N= INT С REND sv9541 RETURN REM жж ENDS UE: xx REM X3 OX X АХ ЖАЖА EE REM БЕМ 3636363 ЖЖ Жы HEH REM жж HECK SUE xXx REM 33 33 09€ 3 0€ ЖҰ EE EH 230 LET DIFF= ABS (G-N) IF DIFF250 THEN PRINT 9a "FR EEZING" 179 250 IF DIFF>25 AND DISF <= 50 T HEN PRINT 95 "COLD" 260 IF DIFF>10 AND DIFF <= 25 T HEN PRINT у» "xWARIME" | 270 IF DIFF>4 AND DIFF <= 10 TH EN PRINT +," ж НОТ жж " 280 IF DIFE>O AND DIFF <= 4 THE N PRINT ss" жж #BCILING# жы" 290 RETURN 700 REM жж END CHECESZLUE xx 210 REM ххх хз ЖЖЖ ЖЕК 220 REM 240 REM 33 CC 30 KHER HEHE HEH GEO БЕМ жж зи Sup ++ SEQ REM хажы ғ HH ED 370 PRINT AT 9.95; "%%%%%7%%%7%%"; TAB 5: "$ SUCCESS %": TAB Si "$5 HEEE ESE" 380 PRINT АТ 10%5: "ІТ TOOK “ITR IES?" TRIES. “ 390 LET MARK =1 400 RETJEN 410 REM жж END SUMCESS Sie жж 420 REN X3X33X3 939 0 HE EK EE Y 430 СЕМ 470 REM жж ЖЖЖ 490 REM жж END/RESUN MOD xx 495 БЕМ 3*3 9 X 3 X 3 30 Ж Жы 200 PRINT ,$4"ANUTHE SO? INPUT Y OR N" SiO INFUT A$ CL 930 IF A$z"Y" THEN GOTO АО 940 PRINT +. "Ok. BYE" wool STOP Se REM xx xx END хх жж The structure of the program is thus: Module 1: 1. Initialise success marker MARK and variable to store number of guesses made (TRIES) 2. Print Instructions 3. Call GET NUMBER Subroutine Module 2 (Main program loop): 1. Increment TRIES 2. Input guess 3. Call CHECK Subroutine 4. Check if Guess equals Number. If it is, then call SUCCESS Subroutine 5. Check marker. If Success subroutine has been called (MARK = 1), then GOTO END/RERUN module 6. Loop back to Input guess again (1) 180 Module 3 (GET NUMBER Subroutine): 1. Define random number 1-99 as number N 2. Return Module 4 (CHECK Subroutine): 1. Set variable DIFF equal to ABS difference of guess and number 2. Check value of DIFF, print appropriate message 3. Return Module 5 (SUCCESS Subroutine): 1. Print success message, number of guesses made 2. Set MARK equal to 1 3. Return Module 6 (END/RERUN module): 1. Print prompt for input 2. Input response to Another go? (A$) 3. If replay required (A$ = ‘‘Y’’) then GOTO Module 1,3 4. If A$ not “Ү” then print end message 5. Stop Notice that (although this is a program that has been modularised rather artificially to demonstrate the principles in a short program) the program consists of an introductory section, then a main program loop with both conditional and unconditional calls to subroutines, within a short main program loop. This makes the structure of the program clear, and minimises the use of GOTO statements, which would be required in profusion if the program were written in a linear, rather than modular fashion. It is perfectly possible to write the program in this linear manner, but the structure will not be as visible. You should also note that the END/RERUN module is not a subroutine, but uses GOTO to pass control to this section from the main program, with a conditional GOTO to pass control back to the main program if required. Conditional GOTOs аге preferable program structures to unconditional GOTOSs, and whilst the END module could be a subroutine, RETURNing to the main program loop, further conditions would need to be inserted to pass control to Module 1 for a new number to be defined. The subroutine would also need to be exited by а GOTO for the program to stop. There is another solution, however, involving a nested subroutine, which we will set as an exercise. Exercises 1 Rewrite /GUESSNUM"' with the END/RERUN module as a subroutine. The procedure should be as follows: END/RERUN SUB i. Prompt for player input, and get response, as before. 181 п. If RERUN not required, bypass 3 апа 4 below, by a GO TO the RETURN line. ш. GOSUB to GETNUMBER subroutine. This is a nested subroutine. The new value of N will be set by this operation. iv. Re-initialise TRIES as 0 and MARK as 0. v. Return. The main program loop is then returned to. The main program must then test whether it is to exit (rerun not required) or continue (new game started). We could set another marker to test this, but in effect we have done this by re-setting MARK ifa rerun is required. Rewrite the main program loop, so that on return from the END/RERUN subroutine, the program loops back only if MARK = 0. If MARK = 1 then the program will not loop back and you can either insert a GOTO to bypass all the subroutines to an end program procedure, or STOP the program before the subroutines. Insert an additional subroutine which prints 1;‘‘ST’’,2; “ND”,3;*°* RD”, and then “ТН” for other numbers into the “FACTORS” program (Unit N2). Write a program which determines how many rolls of a die are required to produce a total score greater than 100. Use subroutines to produce the random numbers for the die rolls and to print out the results. Let the computer choose a four digit number with no two digits alike. You try to guess the number chosen. The computer indicates H (too high), L (too low) or R (right) for each digit in turn and determines how many guesses are required to get the correct number. Use subroutines to create the number, input the operator's guess and give the response to each guess. 182 PART THREE ADVANCED BASIC PROGRAMMING ТАРЫ s ДАЧ ОЛА мМАЯООЯЯ MEAN LOW ATTO А SECTION O: PROGRAMMING METHODS II O1: Résumé Before we enter the arena of advanced BASIC programming let us recap on what we have examined and accomplished so far. The method to design the solution or algorithm to a computational problem using ‘top down’ analysis has been explained. We have seen how to break our problem up into sub-problems which form our program modules (using tree diagrams). We know how to describe the algorithm in concise English sentences that we call pseudocode and how to determine and illustrate the flow of control in the problem solution by drawing a flowchart. When designing our solution we recognise the need to use the fundamental programming tools of: (1) decision making (п) branching as a result of decisions (iii) direct transfer from one point in the algorithm to another (iv) repetition These control structures, as they are called, which are present in all computer languages, have been discussed in some depth, together with other important BASIC language fundamentals. The techniques of: (1) decision making (п) numeric processing (iii) character handling with strings (iv) looping through counting and condition testing (v) handling of output by printing and plotting and the realisation of modular techniques in programming by using subroutines have all been covered. WHAT'S NEXT? We must now consider the second phase of the programming method - producing the program itself. It 1s important to do so at this stage in the book, so that our programming tool kit is complete enough to investigate and use the more sophisticated information handling facilities to be introduced later in this section: (1) logical operations on data (1) character codes (uni) moving graphics (iv) graph plotting (v) constructing and searching lists and data arrays (vi) how to sort information into order Once these skills have been mastered our complete programming expertise can then be applied to real applications. Let's now see in this section of the text how to code our algorithms into BASIC language programs, and then debug, test and document them. 185 Further important design rules will be given, and finally a summary of our complete programming method will be provided with a flowchart and worked example. O2: Producing the Program We now consider the method by which a well designed, tested and fully documented program is produced. Given our algorithm - which we have written out in steps in a description we call pseudocode — together with our flowchart — which shows how the steps of the solution are combined in sequence for the computer to solve the problem - we must now: 1. CODE THE ALGORITHM IN SINCLAIR BASIC 2. DEBUG AND TEST THE PROGRAM 3. DOCUMENT THE PROGRAM O3: Coding and Design CODE ON A ONE TO ONE BASIS If the description of the algorithm is correct then coding on an almost one to one basis from statements in the pseudocode or the flowchart is possible. If you cannot code from the flowchart or pseudocode then further refinement of the algorithm is necessary. Pseudocode descriptions in formal mode of the BASIC language control structures for decisions and loops are given later in this section. You will notice that the description itself is indented and concise, with the terms almost the same as BASIC statements. This is not unusual as BASIC was designed to do this very thing and 1s English-like in its syntax. To be able to code at all you must of course: KNOW THE BASIC LANGUAGE AND ITS RULES Hopefully it is the right language for the job. On the ZX81 and Spectrum you don't have much choice! Actually it is a question of ease of programming specific applications that generates different languages. Most things can be done in BASIC, although perhaps not efficiently or elegantly. It is often useful to identify the kind of processing that will be required. When designing the algorithm consider whether the problem is a scientific or a business application, whether extensive calculations will be performed or large amounts of list processing done, whether the data is extensively numeric or string and whether the program will be interactive with much user dialogue. When coding, avoid spelling and formatting mistakes. Sinclair BASIC is powerful in that it is one of the few available single keystroke 186 BASICs, hence you cannot make spelling mistakes on instructions or commands because the whole instruction is keyed in at once. However, mistakes can still be made when assigning variable names and in PRINT and REM statements. DEFINE AND CONTAIN EACH MODULE WITH REM STATEMENTS For example: 100 REM * SORT MODULE * 200 REM * THIS MODULE SORTS STRINGS * 500 REM * END SORT * TERMINATE YOUR PROGRAM PROPERLY You may have noticed that Sinclair BASIC does not need a special end-of-program statement. We can, however, put one in using a REM statement. For example: 500 REM * END OF PROGRAM * Тһе 7Х81 and Spectrum do not process but only note REM statements. When the above line runs, the program will finish elegantly with a 0/500 message. We can also stop a program with the STOP statement. Main modules should finish like this with subroutines programmed at higher line numbers terminated with a REM * END * statement. When terminated with STOP a message 9/line number (a 9 Stop (Line number): 1 statement on Spectrum) will be given. REM * NAME OF PROG * 10 REM * MAIN MODULE * 20 GOSUB 500 30 STOP 40 REM * END MAIN * 500 REM * SUBROUTINE * 600 RETURN 700 REM * END SUBROUTINE * 800 REM * END OF PROGRAM * We could also use a GOTO 800 at line 30 to terminate execution on the last program line. ALWAYS CODE ACCORDING TO THE LOGICAL ORDER OF PROCESSING This is usually ensured if you code from a flowchart, with your 187 flowchart structured into modules, i.e. flowchart groups for the modules in the program. Take care with the control structures and avoid unnecessary branching, especially with GOTO instructions. Try to make your programs both readable and efficient — but first make them readable! USER FRIENDLY PROGRAMS Design your programs with the user in mind - and that includes you! Directions to users should be concise and as few as is necessary, both in the program and in the user guide if your program is large enough to merit one. Where the user needs a number of instructions to operate the program then these can be built into an optional ‘help’ module or subroutine. 100 REM * USER INSTRUCTION * 110 REM * DIRECTS USER TO HELP SUBROUTINE * 120 PRINT “ FOR INSTRUCTIONS TYPE HELP OTHERWISE TYPE C " 130 INPUT A$ 140 IF A$ - *HELP''THEN GOSUB 1000 150 REM * END USER INST * 1000 REM * HELP SUBROUTINE * 1200 RETURN 1210 REM * END HELP * Users usually require to know: ~ how to run the program — what form of input data is required — what output is produced Your program should check on the range and type of input data. If the input data is out of range or incorrect the program should not stop with an error, but continue with a message to input correct data. After you have designed a program to do a specific task it may be worthwhile to change it to be as general as possible — i.e. do several similar tasks. As you become more skilled and confident in programming you will be able to generalise and write a subroutine that enables users to select options from a menu. This is exactly similar to the exercise you have seen in multiple decision structures. See the "CASSFILE'' program in Section V, for a ‘‘menu-driven’’ program. More “‘user-friendly’’ tips are given in the section on documentation, and some useful routines in Unit V2. 188 DESIGNING PROGRAM LAYOUT You must make your program readable. The program design will be modular and contain specific identifiable segments, subroutines and modules. These should be labelled in the design of the algorithm and transferred in the coding process. (1) EACH MODULE SHOULD BE TITLED AND LABELLED TO INDICATE ITS FUNCTION. FOR EXAMPLE: 10 REM “AVERAGE” 20 REM * PROGRAM AVERAGES ANY NUMBERS INPUT * 3 REM * 40 КЕМ * USER ROUTINE * 50 REM * CHOICE OF NUMBERS INPUT * 60 PRINT “HOW MANY NUMBERS DO YOU WISH TO АУЕКАСЕ” 70 INPUT N 80 DIM A(N) 9) REM * INPUT ROUTINE * 100 REM * NUMBERS INPUT TO ARRAY * 110 PRINT “INPUT NUMBERS" 120 FORI=1TON 130 INPUT A(I) 140 NEXT I 150 REM 160 REM * PROCESSING ROUTINE * 170 REM * COMPUTES AVERAGE * 180 LET SUM-0 199 FORJ=1TON 200 LET SUM = SUM +A(J) 210 NEXT J 220 LET AVERAGE - SUM/N 230 REM 249 REM * OUTPUT ROUTINE * 250 PRINT “THE AVERAGE OF" 260 FOR K=1 TON 270 PRINT A(K); ”’; 280 NEXT K 290 PRINT “IS ”; AVERAGE 300 REM 310 REM * END AVERAGE * (2) DESIGN YOUR PROGRAM SO THAT RELATED STATEMENTS ARE TOGETHER For example, input — processing — output statements: () All input statements will be at the beginning of a simple sequential program, processing in the middle, and output normally at the end. 189 (3) (4) (9) (üu) For a modular program, input, processing and output routines will be separate modules or groups of statements within a single module. (ш) Subroutine modules will usually be placed separately at the end of a program. INSERT REM STATEMENTS BETWEEN PROGRAM MODULES AS SEPARATORS Program modules are then easily identified. Use blank REM lines or lines of asterisks. PLAN YOUR PROGRAM LAYOUT BEFORE CODING The printed listing of your program is important. Choose a maximum line width. Break longer lines into shorter ones in REM statements by using spaces. Compensate for overrun. For example: 10 REM * AAAAA AAAAA AAAAA * You will not be able to do this with other BASIC statement lines. YOUR LAYOUT SHOULD TRY TO REFLECT THE MODULAR STRUCTURE OF YOUR PROGRAM 190 Indented statements are not possible on the ZX81 or Spectrum, unfortunately! DESIGNING PROGRAM OUTPUT For the user the output is the most important part of the program. Take time planning it. The output instructions in Sinclair BASIC are: PRINT, PRINT AT, PLOT, LPRINT, COPY, TAB, plus graphics commands. () RESULTS SHOULD BE OUTPUT WITH RELATED ITEAL Label all your numerical output: єн. 1974 £5678.65 instead of 1974 5678.65 e.g. AVERAGE AGE OF BOYS IS 15 YRS 3 MONTHS rather than 15 3 (i) DISPLAY LARGE AMOUNTS OF OUTPUT AS A TABLE, HISTOGRAM OR GRAPH, AND GIVE TITLES. For example: TABLE 1: NET INCOME FOR B. JONES FOR YEARS 1978-80 Box your tables if possible. The user should not have to look up the program listing to see what the numbers in the output mean. au) DESIGN YOUR OUTPUT TO BE EASY TO READ Plan it to be attractive to any user of your program and, of course, yourself. Graphics is a powerful tool for this. (iv) ALIGN, SPACE AND JUSTIFY THE OUTPUT Plan your output with reference to the screen size and divisions. For tables — align information central to the heading align signs right justify numbers left justify characters. (There are routines in the text for doing this). For example: 876-340 JIM SMITH 27-210 HUNG FO 453-003 SARAH JAY 1-025 DRACULA NUMBERS 15.003 815.231 - 4.000 – 100.100 Fill in with zeros to get decimal placing correct. (v) USE SPACE CAREFULLY Sinclair computers use expensive printer paper! Print output horizontally wherever possible. For example: TABLE OF POWERS OF 2 2 4 8 16 32 etc should be: TABLE OF POWERS OF 2 2 £ 8 16 32 64 128 256 512 1024 (vi) DO МОТ OVERDO EXPLANATIONS Be succinct! (уп) MAKE YOUR ABBREVIATIONS CLEAR x = 25 NDTC =25 NUMBER OF DAYS TO CHRISTMAS = 25 (vii) DISPLAY INPUT DATA AS AN OPTION Allow checking of input data before processing. Make your program check for incorrect or bad input data. MODULAR DESIGN We break problems down into sequences of steps to produce programs in which different kinds of activities are separated out. These distinctive program modules are our SUBROUTINES or SUB- PROGRAMS. Each module has its own name and address, but in BASIC we usually refer to program modules by address only, as with: GOTO 100 and GOSUB 3300 where the address is the line number of the first statement in the module. We can address sub-programs or modules by name by assigning the name and address of the module at the start of the program. For example: 10 REM * ASSIGN MODULE NAMES * 20 LET INPUT DATA = 1000 30 LET PROCESSING = 2000 192 40 LET OUTPUT DATA = 3000 59 REM * END MODULE ASSIGN * 60 REM 70 REM * MAIN * 80 GOTO INPUT DATA 90 GOSUB PROCESSING 100 GOTO OUTPUT DATA 110 STOP 1000 REM * INPUT DATA MOD * 1500 GOTO 90 1600 REM * END INPUT * 2000 REM * PROCESSING SUBROUTINE * 2500 RETURN 2600 REM * END PROCESSING * 3000 REM * OUTPUT DATA MOD * 3500 GOTO 110 3600 REM * END OUTPUT MOD * 4000 REM * END PROG.* There are good reasons for modular design and the use of subroutines and sub-program modules. The logic of the program, i.e. its flow, is easier to follow. The clarity of the structure of the main program is improved whilst program design is proceeding by referring to the number or name of the module initially, instead of starting to write out the code of the module at that point. The module can be coded as a separate entity. Independent testing of modules is possible, but care must be taken that all variables have been declared and have their correct values at the start of the module. Debugging 1s simpler with this approach, since the module is isolated. You can leave the coding of a module until a later stage, but you must know what it will do when coded. If a module has to be used several times in a program from different places it need only be written once and called (into action) from these points by reference to its line number or name. 193 Program modules can be designed to run sequentially: START MODULE 1 INPUT MODULE 2 PROCESSING MODULE 3 OUTPUT STOP This structure is convenient for simple programs. However, programs can be structured in terms of subroutines and sub-programs being called from a short and simple main program module. START MAIN a MODULE MODULE 2 MODULE 3 194 This structure is convenient for longer, more complicated, programs with many modules and nestings. Subroutines automatically return to the next line in the main program through the RETURN statement. Other modules are called by GOTO (line number) and return by GOTO (line number) instructions. GOTO MUST BE USED WITH THOUGHT AND CARE AND NOT EXCESSIVELY. Use a GOSUB unless a return to a different point in the main module is needed or a multiple return is possible as a result of a decision to be made within the module. Nested modules can be treated as other modules and called from within the subroutine or sub-program, by GOSUB and GOTO instructions. Nested loops must be contained within the same module, however. CONTROL STRUCTURES IN SINCLAIR BASIC (1) Each control structure is a program module. (2) A formal pseudocode description of each structure is given of the general form of the control structure. (3) A flowchart description is given of the general form. (4) The BASIC version is given of the general form. (5) A simple example illustrates the BASIC form of the control structure. (6) Structures will be written in indented form in the pseudocode version for clarity. You cannot indent in Sinclair BASIC program listings. REM statements must be used to show the start and stop lines for program modules. (7) P is a processing operation. It can be a single instruction, a statement or a group of statements. (8) In the formal pseudocode each structure will commence with the title module (abbreviated to mod), and end with the statement endmodule (abbreviated to endmod). (9 In BASIC cach structure will be bounded by REM*STARTMOD* and REM*ENDMOD* statements. (10) Flowcharts will be bounded by START and STOP symbols. The structures summarised are: A) Decision Structures (1) Single decision IF-T HEN structure (п) Double decision IF-T'HEN-else structure (ш) Multiple decision Case structure 195 B) Loop Structures (i) repeat-forever loop structure (ii) repeat-until structure (iu) while-do structure (iv) FOR-NEXT structure The names of the structures are implemented as actual programming language structures in other languages and some forms of BASIC. The FOR-NEXT structure is a special form of the while-do loop, given a specific implementation in BASIC. A. DECISION STRUCTURES () SINGLE DECISION: The IF-THEN structure Meaning: IF (condition is true) THEN (do something) Pseudocode Flowchart mod if (condition) then P endif endmod BASIC 10 REM*START MOD* 20 IF (COND) THEN P 30 REM* ENDMOD* Example Input a number and if it is positive, print it. Pseudocode BASIC mod 10 REM*START MOD* input A 20 INPUT A If A > Q 30 IF A>@ THEN PRINT A then print A 40 REM*END MOD* endif endmod 196 (i) DOUBLE DECISION: The IF-THEN-else structure Meaning: IF (condition is true) THEN (do something) otherwise (if condition is false) do something else. Pseudocode Flowchart START mod if (cond) then P1 else P2 endif endmod BASIC 10 REM*START MOD* 20 IF (COND) THEN GOTO 50 30 (FALSE TASK P2) 40 GO TO 60 50 (TRUE TASK P1) 60 REM*ENDMOD* To perform the true task (P1 in the pseudocode) first, the BASIC implementation of the structure would test the complement of the condition, so that in the program below, for example, A>B would be replaced by A<B, and lines 50 and 70 swapped. Note the standard form of complement would be B< = A, but we have defined the input numbers as unequal in this case. 197 Example Input two unequal numbers and print the largest. Pseudocode BASIC mod 10 REM*STARTMOD* input A,B 20 INPUT A ifA>B 30 INPUT B then print A 40 IF A» B THEN GOTO 70 else print B 50 PRINT B endif 60 GOTO 80 endmod 70 PRINT A 80 REM*ENDMOD* (ш) MULTIPLE DECISION STRUCTURE: The case structure With this structure we want the program to select and perform one of several alternative tasks. The conditions in this case structure are sequential, not nested and mutually exclusive. Pseudocode Flowchart mod case if (condition 1 is true) then P1 if (condition 2 is true) then P2 if (condition 3 is true) then P3 end case endmod 198 BASIC 10 REM*STARTMOD* 20 IF Cl THEN P1 30 IF C2 THEN P2 40 IF C3 THEN P3 320 REM*ENDMOD* Example Test whether a number input is positive, zero, or negative, and print the result. Pseudocode Flowchart mod input A case PRINT if A<0 NEGATIVE then print “МЕСАТІУЕ” If А = 0 then print “ZERO” if А>0 then print “POSITIVE” endcase endmod PRINT d PRINT POSITIVE 199 BASIC 14 REM*STARTMOD* 20 INPUT A 30 ЕА < 0 THEN PRINT “NEGATIVE” 40 IF A-0 THEN PRINT “ZERO” 5) IF A>@ THEN PRINT “POSITIVE” 60 REM*ENDMOD* Alternatively, we can use conditional and unconditional GOTO statements to implement this structure. This would be appropriate if the processing section of a program after the decision were several statements long, rather than the single instruction available on the ZX81. Spectrum users can add more instructions on the same line. They should be restrained in using this facility. 10 REM*STARTMOD* 20 INPUT A 30 IF A< 0 THEN GOTO 60 40 IF A-0 THEN GOTO 80 50 IF A>@ THEN GOTO 100 60 PRINT “NEGATIVE” 70 GOTO 110 80 PRINT “ZERO” 90 GOTO 110 100 PRINT “РОБІТІУЕ” 110 REM*ENDMOD* В. LOOP STRUCTURES (1) The repeat — forever loop Meaning: None. The only conceivable result is the program halting with an arithmetic overflow report. Pseudocode Flowchart BASIC (такт) 10 REM*STARTMOD* START 20 P 30 GOTO 20 mod 40 REM*ENDMOD* repeat P forever endmod 200 (i) This structure is for demonstration only. Avoid using it in programs! It can sometimes occur in error. Use BREAK if you suspect your program has entered such a loop (because nothing happens). The repeat — until loop Meaning: Repeat processing until a condition is true. These structures loop until a specific termination condition is met, for example until a counter reaches a certain value or until a dummy or sentinel value 1s input. The important characteristic of this loop structure is that the repeat test (or exit test) is at the bottom of the loop, after the processing ‘body’. The program lines making up the body of the loop (P) will be executed at least once. The repeat condition can use any conditional operator or its complement (reverse). e.g. equals 4—0 not equal - <> Use of the complement often leads to a more elegant program. Pseudocode Flowchart mod repeat P until (condition is true) endmod BASIC 10 REM*STARTMOD* 20 P 30 IF (COND) THEN GOTO 50 40 GOTO 20 50 REM*ENDMOD* 201 BASIC using complement 10 REM*STARTMOD* 20 P 30 IF (COMP COND) THEN GOTO 20 40 REM*ENDMOD* Exit requires no specific instruction. Example Input and print strings until the sentinel value “LAST” is input. Pseudocode Flowchart START mod repeat INPUT Ag input A$ print A$ until A$ = LAST endmod PRINT Ag Ag-LAST ? BASIC 10 REM*STARTMOD* 20 INPUT A$ 30 PRINT A$ 40 IF A$=‘‘LAST’’ THEN GOTO 60 50 GOTO 20 60 REM*ENDMOD* 202 Complement Version 10 REM*STARTMOD* 20 INPUT A$ 30 PRINT A$ 40 IF A$<>‘‘LAST’’? THEN GOTO 20 50 REM *ENDMOD* (ш) While — do structure Meaning: While a condition holds (TRUE) keep repeating the process until the condition is broken (FALSE). The condition can be, for example, that a loop-counter variable value is not equal to its final value (IF N<10 THEN..). The process will then repeat until it is. The condition may also be set so that a sentinel value has not occurred (IF N<>6 THEN). These conditions are set so that the true pathway is the process task, and the false is the exit. The While — do loop is characterised by having the repeat test carried out prior to the body of the loop (i.e. at the top). No processing will happen if the repeat test is false at the first encounter, i.e. the body of the loop is never entered. Pseudocode Flowchart START mod while (condition is true) do P endwhile endmod BASIC 10 REM*STARTMOD* 20 IF (COND) THEN GOTO 40 30 GOTO 60 40 P 50 GOTO 20 60 REM*ENDMOD* 203 (iv) Using the complement of the repeat condition gives a neater program. Complement Version 10 REM*STARTMOD* 20 IF (COND) THEN GOTO 50 P 40 GOTO 20 50 REM*ENDMOD* Example While the value of the square of consecutive integers is less than 100, print them on the screen. Pseudocode BASIC (complement) mod 10 REM*STARTMOD* п = 1 20 LETN=1 while п*п< = 100 30 IF N*N>100 THEN do print n*n GOTO 60 n=n+1 40 PRINT N*N 45 LET N=N+1 end while 50 GOTO 30 endmod 60 REM*ENDMOD* FOR - NEXT Loops FOR - NEXT loops are a special BASIC structure for repeating a process a stated number of times. They are in fact While — do loops and have the repeat test at the top of the loop. Example Print the values of the first ten integers. Pseudocode BASIC mod 10 REM*STARTMOD* n= 1 20 FOR N=1 TO 10 While n < = 10 30 PRINT N do print n 40 NEXT N п=п+1 50 REM*ENDMOD* епа while епатоа FOR - NEXT loops have their own special flowchart symbol, because they are used so extensively in BASIC: 204 Ordinar Special This is a condensed version. It groups together the FOR — NEXT — STEP instruction elements, which the standard form separates. This illustrates both a While do and a FOR- NEXT structure. O4: Program Development Program Development involves the activities of DEBUGGING your program of errors, TESTING to see if it behaves as specified and gives the desired results, and DOCUMENTATION which tells users how to run the program. DEBUGGING The Sinclair machines have good editing facilities and error messages. Those on the Spectrum have brief statements of the error type, those on the ZX81 have just a number or letter. Although it is inefficient to correct errors one at a time (because there is seldom only a single error since programming mistakes tend to compound one another), error messages on the machine are produced singly, since an error stops the computer from running. Thus we must deal with the errors as they occur in the program sequence. You may notice a number of errors on carefully looking through the listing. Any you spot should be edited out at once. GET TO KNOW YOUR COMPUTER ERROR CODES This will happen automatically in time (as you make mistakes!), but it is worthwhile studying the codes. They define the ways in which 'run- time' errors occur, and an understanding of them will help you avoid bugs. 205 EXIT Keep a note of mistakes you have made and how you corrected them. This will be valuable for future reference. This should become an automatic part of your personal documentation. Keep a copy of old program listings. Record the errors you have made, the corrections you tried but which did not work, and what you learned in developing the program. Trace the impact of any error through the program. SYNTAX ERRORS These are caused by BASIC statements you key in which do not obey the precise language rules (syntax rules) of Sinclair BASIC. The syntax errors are detected by the LINE INTERPRETER which automatically checks each line you key in when you press the NEWLINE (ENTER) key. If there is an error the interpreter will place the SYNTAX ERROR cursor just before the first error it detects on the line. This may be at the end of the line if the interpreter finds that something else should have been placed there. To correct this type of error you must compare the syntax you have written with the rules of BASIC. Typing instructions incorrectly cannot occur on the Sinclair computers as the BASIC 15 single key-stroke. In other BASICs you must type P,R,I,N,T, for PRINT. Instructions in general are automatically placed in the correct order along a line (i.e. the order of line number - instruction — operand), since they are taken care of by the mode controller which sets the cursors in the correct sequence. Errors which can occur are: 1 Omission of line number Line number too large (29999) Line number negative Line number non-integer Omission of delimiters: brackets (must be paired) commas semicolons quotes colons (on the Spectrum) 6 Typing in of improper variable names 7 Incorrect logical expressions There can be more than one error per line. The S-cursor will re-appear in the line when you try to enter it into memory. The line edit facility is comprehensive and easy to use on the ZX81 and Spectrum. You must correct your mistakes, and keep trying to ‘compile’ the line into correct BASIC syntax (to be entered into memory). When successful, the program line will appear at the top of the screen. The syntax error check ensures no nonsense lines (from the computer's point of view) are entered. It cannot help you in coding correct sequences of program lines, or prevent logical errors. сл ны оо ho 206 PROGRAM LOGIC ERRORS These are the effect of bad logical design of the program. They can be avoided if care is taken in the design and coding of the program. Ifa program produces incorrect results then there is an error in the flow of logic in the program. This may only occur with certain values of data. If each program section or module has been tested independently then the linking of the modules is incorrect. We can test program sections as follows: 1) Insert a temporary breakpoint into the program, at the appropriate point. 2) Print out values of intermediate results, to the screen or printer. 3) It is most important to print out the values of variables used in making a decision and those used in loops, either counter loops or FOR - NEXT loops. 4) Go back to the pseudocode or flowchart and modify the steps which are in error. ‘Walk through’ the algorithm, using a flowchart, to check the step sequence, and hand trace the program with selected values of data and/or variables. Be careful! Often changes in one part of the algorithm cause changes in the others. It is no use solving one problem if it causes another! 3) Change the documentation if necessary. Note down the changes you have made, or lines you have deleted. Keep program listings. 6) Re-test the complete program, using a variety of data. Each testing statement in a complex program should be headed by a remark statement. 1000 REM - DEBUG — (Testing Statements) - REM - END DEBUG These temporary REM statements are later deleted by keying in their line numbers, as are the testing statements. It is very easy to leave in test instructions unless they are marked. INSERTING BREAK POINTS We can stop a program at any point and obtain the values of variables, expressions, etc. to test calculations or check for errors. We do this by 207 Inserting a group of statements which will output the values we want and then stop the program. qM < ADD TEST OUTPUT OF VARIABLES МШ < INSERT STOP STATEMENT CONT will restart the program. Individual modules or sections of program can be tested this way. We do, of course, have to RUN the program from the required module line number. Care should be taken when this is done that variables needed in the module have been declared properly and that the values of parameters passed to the module are as required. Remember that you can INPUT the values of variables directly if necessary, using the command mode, and using LET statements: LET X(2) = 20, etc. The value of any variable at the point the program crashed can also be obtained by keying a statement without the line number, and again using the computer in command mode: PRINT A$ LPRINT X(3) The commands RUN N (where N is the line number we wish to run the program from) and GOTO N enable us to run the program starting at any point. Using GOTO N does not negate the initialisation of variables that occurs 2 the program has already run. For example, if we input: 10 LET A=1 20 LET B = 2 39 PRINT A,B and then key in GOTO 30, we get the error report ‘2/30’ (ZX81) or ‘2 Variable not found 30:1' (Spectrum) meaning an undefined variable was found. If we RUN the program, we can then use GOTO 30, and the program signals successful completion. RUN-TIME ERRORS These are a result of programmer carelessness and do not prevent the interpreter from translating the program. They make the program crash when you attempt to run it, that is they prevent the program from running to completion. Common run-time errors are: 1) undeclared or unidentified variables 2) arithmetic overflow 3) lack of data for processing 208 4) failure to complete loop increment and subroutine section statements 5) subscript out of range 6) memory full 7) screen display file full 8) integer out of range As we have seen, run-time errors cause diagnostic system messages to be printed. ‘These appear at the bottom of the screen and are called: ERROR CODES These errors can then be traced through the type of error given by the code and the line number at which the program stopped. ERROR CODES Error codes or Report codes are presented on the screen when a program stops for any reason, either as a result of successful completion (no more program lines), an instruction or command (STOP, BREAK), or a run-time error. On the ZX81 the codes have the form E/N, where E is the code for the type of error and N is the line number where the program was stopped (STOP or BREAK), or where an error occurred. N is @ fora direct command. This is an example of an error code on the ZX81 which is printed on the screen when an arithmetic overflow (number larger than about 10% generated) occurs in line 60 of the program: 6/60 The Spectrum gives an extended error report code, with a brief statement in the form: E Statement N:S where E is the report code, the statement is the reason for stopping (with BREAK or STOP or program completion) or type of error. N is the line number, but since the Spectrum can have multiple line statements, the S number indicates which statement on the line the report code refers to. We are not using multiple line statements in this text, so S will always be 1, meaning the first (and only) statement on the line, unless after the THEN in an IF... THEN statement, which 15 treated, like a colon, as a statement separator. The Spectrum's version of the example given above (the ZX81’s arithmetic overflow error code) is: 6 Number too big 60:1 Report codes are crucial aids to debugging programs. Without them we would know only that we had an error, but not where it occurred or what type of error it was. The error reports indicate both of these items of information. It is important to understand that the cause of an error may come earlier in a program than the line where the program stopped. For example, a code 2 error (variable not found), occurring in line 100 of a program might be caused by a mis-spelt variable name in line 100 (not 209 the same as the variable you meant it to be — putting GUES when you meant GUESS, for example). It could also be the result of not having assigned the variable earlier in the program. If the error causing the program to halt is not apparent from the line given in the error report, the program flow must be traced backwards to find the prior cause. In some cases this can be extremely difficult to track down - for example, where a numeric value wrongly defined or generated by the program causes another expression to cause an arithmetic overflow. Tracing techniques must be used. Lists of Error codes and their meanings for the ZX81 and Spectrum are given in Appendix II. TESTING AND VERIFICATION Verify that your program works by testing it with Test Data Testing comes after debugging a program. Its purpose is to ensure that the program is logically correct, produces correct answers and meets the specification of its purpose. 1 First test each module separately Each procedure and subroutine should be treated as if it were a separate program. Test for (i) good data - the expected type and range of inputs. (1) bad data — out-of-range and incorrect type inputs. Try to ensure each procedure ‘fails softly’. For bad data (particularly in any data entry module) following each input a check routine or procedure should be used to give an error message if range is incorrect or check type of input and correct syntax. This is best done with strings, which are more flexibly handled. See Unit V which deals with input checks at length. 2 Combine the modules and test the complete program If there is a logical error (1.e. program does not produce the intended results) insert additional test statements which will: (i) Output intermediate results. (11) Output values of variables at each stage. (iii) Output results of expressions at each stage. (iv) Output values of the loop counter at each pass. (v) Output results of array manipulation after each operation. (vi) Output values of parameters before and after subroutines entry and return. 3 Handle exceptions (1) Test all data in the program. (11) Screen all data. (111) Process only good data. (iv) Output bad data saying why it was bad. 210 4 Let your program stop elegantly (1) When there is no data input or data available, the program should tell you so. (1) Sinclair BASIC programs are interactive. The user сап control program continuation with: 910 PRINT “PROCESSING ENDED - MORE DATA? ANSWER YES OR МО” 920 INPUT A$ 930 IF A$ = “YES” THEN GOTO 100 940 PRINT “GOODBYE” 950 STOP 960 REM PROGRAM END 5 Rewrite the program until you are satisfied with it Remember the program should be - structured — easy to read — easy to understand — handle exceptions — be as efficient as possible — documented and it must solve the problem as specified! 6 Put clarity before efficiency To be good a program algorithm does not have to be clever, difficult to understand or run super-fast. If you do not understand how the algorithm works do not use it — rewrite and re-design or use another method. Programs will work correctly if the rules of the language are obeyed, and the program will work to specification if the algorithm 1s properly designed. DOCUMENTATION ANNOTATE AND DOCUMENT YOUR PROGRAM AND CREATE A READABLE PROGRAM 1 Write an explanation for each program module or segment. At the beginning of each segment provide suitable comments which explain: (1) the purpose of the algorithm (2) the variables and their significance (the values they store) (3) the results expected. 2 Use comments only where necessary: (1) don't comment each program line (2) don't explain the obvious (3) at the beginning of the program provide a block of 211 10 comments that explain the program at each module and provide a comment which explains what the module does in relation to the program. Clear comments should appear separated from program code. The clearest comments are framed. For example 19 REM * * * * * * * * 20 REM * SUBROUTINE TO * 30 REM * CALCULATE N TO 2 D.P. ы 40 КЕМ * i 50 REM * * * * * * * * Lines of asterisks provide visible dividers between sections of program. Use comment in the program and in the output to the screen or printer. Use blank REM lines as separators in the program. For large programs write a reference document: (1) Describe the algorithm you used. If it is not original you should include a note of its source, author, version, and type of computer it was written on. (ii) Explain how you wrote the program, the reasons for writing it, the type of computer used and memory required. (ii) Make a note of areas that may need improving, or could be modified for different purposes. (iv) Which modules are general (menus, subroutines), and which require specific kinds of input. (v) Explain the scope and limitations of the program. (vi) Include your name, and the date of production. List the tests you made and data used. Reproduce some of the results of the tests. List performance tests (e.g. how long it takes the program to run). Give user instructions and reproduce the output of a run and explain to the user how he uses the program. Give the program characteristics. Explain any abnormal behaviour of the program (e.g. response to bad input). Write a brief USER GUIDE. This is mot for the computer expert. It should explain: — the purpose of the program — the algorithm — how to run the program — what input is needed — what results are printed — how to use the menu (if included) O5: THE COMPLETE PROGRAMMING METHOD SUMMARY: THE STRUCTURED PROGRAMMING METHOD 1. | PRODUCE THE ALGORITHM State the Problem fully 1.4 1.3 1.3 1.4 1.1.4 1,2,2 State the problem Understand what is to be done Research the Problem 1.2.1 1,24% 15,4 Research апа analyse the problem to see how the computer can handle it Identify all formulae and relations to be used. Identify all data involved Design the algorithm Use top down structured methods: 152,1 1,5,2 1.5.3 1.3.4 1.2.9 1.3.6 Break the problem up into sub-problems ог modules. Use a structure diagram or tree diagram to help in breaking down the problem. Start classifying modules or parts of modules as: INPUT PROCESSING OUTPUT Utilise the fundamental control structures in the modules — Decision structures — Transfer structures — Loops - Subroutines - Nested structures — Subprograms Set up a DATA TABLE in which all data types are classified as Variables Constants Counters Functions - if using a Spectrum and the DEF ЕМ instructions Define the algorithm further until coding it into a BASIC language program is an easy and obvious exercise. Describe the algorithm in Pseudocode and Flowchart form 1.4.1 1.1.2 1.4.3 Write out the final algorithm (now in modular form) in small steps in an abbreviated English style called Pseudocode. Each module should be treated separately and !abelled. Illustrate the logical flow of control in the algorithm by constructing a flowchart. Test the algorithm, if necessary using a hand trace or walk through. 213 2. 2.1 Code the Algorithm in SINCLAIR BASIC 2.1.1 Code on a direct basis from the pseudocode or flowchart description in line numbered BASIC statements, module by module. 2.1.2 Implement the fundamental control structures, used in their SINCLAIR BASIC versions. 2.2 Debug and Test the Program 2.2.1 Debug the Program. Check the program variables against your algorithm test. Correct syntax, run time, and logical errors. 2.2.2 Test the program for further logical errors. Run the program with sample data. 2.3 Document the Program For a full documentation, you should: 2.3.1 Produce a programmers’ guide consisting of: pseudocode flowchart variable table or data table program listing test results or sample printout. 2.3.2 Detail the steps that producing the program involved. 2.3.4 Write a user guide. 214 PROGRAMMING: SUMMARY OF METHOD IN FLOWCHART FORM This provides a diagrammatic version of the summary of structured START FIND OUT WHAT YOU HAVE TO DO. programming: STATE THE PROBLEM DRAW A STRUCTURE DIAGRAM OF HOW YOU ARE GOING TO SOLVE THE PROBLEM. (THE ALGORITHM ) WRITE A DESCRIPTION OF THE ALGORITHM. PRODUCE A FLOWCHART CONDUCT A WALKTHROUGH ERRORS ? No В) 215 CODE INTO BASIC FIND ERRORS AND CORRECT RUN A TEST ERRORS ? No TEST FOR RUN TIME & LOGIC ERRORS DOES IT DO WHAT YOU WANT IT TO DO? No Yes IS THERE MORE YOU NEED TO KNOW ABOUT THE PROBLEM? TEST FOR EXCEPTIONS & GET SOMEONE ELSE TO TRY IT OUT. THIS PROBLEM NEEDS A RE-THINK. PUT EVERYTHING ELSE ASIDE, AND DON'T RUSH ERRORS 2 No WRITE DOCUMENTATIO OF HOW IT WORKS, FLOWCHARTS AND DOCUMENTATION OF HOW TO RUN THE PROGRAM. END AN EXAMPLE OF STRUCTURED DESIGN 5 2. 2. 4. Problem Statement Write a program that computes and prints the Average or Mean (M) and Standard Deviation (S) of a collection of N data items. To compute SŠ use the formula: Standard Deviation = Sum of Š A of Items) _ (Mean) Find out what we have to do (research the problem) We are given most of the information in the question but we are missing some. It does not tell us how to compute the Mean or Average. This is given by the formula: (Sum of all numbers) Mean = N We now have all the information, we need to start designing the algorithm. What is involved in this problem The outline procedure we can now define: a) We have to INPUT the numbers, and b) Perform two calculations on these numbers. First we calculate the Mean and then use the Mean value to calculate the Standard Deviation, then c) Output the results. Design the algorithm This gives the detailed procedure for the steps needed to solve the problem: a) INPUT The numbers are going to be input into an array because they will be needed twice in the calculation module. b) 1. Calculate: the Mean — Add all the numbers in the array and divide by N. 2. Calculate: the Standard Deviation - Total the squares of all the numbers in the array. Use the formula to calculate S. c) Output: the Results — The results will be printed on new lines with the words MEAN = and STANDARD DEVIATION = followed by their values. 217 5. The Tree Diagrams 1. Compute and print Standard Deviation and mean Results Each of modules 1.1, 1.2 and 1.3 will be subroutines. These will be called in the appropriate sequence by the main program module. INPUT 1.14.2 1.143 ASK HOW MANY INPUT N NUMBERS NUMBERS AND INPUT N 1.1.1.1 DIMENSION 1.1.3.2 ARRAY ; FOR I-1 TO N, Y(50) INPUT Y(I) FIND MEAN AND STANDARD DEVIATION 1.2.4 1.25.34 ^ c CALCULATE STANDARD FIND MEAN DEVIATION 1, 2.1. 2 SUM ALL DIVIDE SUM BY NUMBER ELEMENTS OF ELEMENTS FOR I = 1 TO N LET MEAN = SUM DIVIDED BY N LET SUM = SUM + Ү(І) 218 1.2.2. CALCULATE STANDARD DEVIATION 1.2.2.1; ls£s2. 2. CALCULATE SUM OF USE FORMULA TO THE SQUARES CALCULATE STANDARD DEVIATION ГЕ ТУРУР PI UM PX INITIALISE FOR EACH VARIABLE ELEMENT GET SQUARE, ADD TO TOTAL LET SUM HN FOR I=] SQR-SUM TO N SQR«Y(I) **? ( f ON SPECTRUM) Led OUTPUT RESULTS lesel PRINT "MEAN = "; MEAN 1.3.2 PRINT "STANDARD DEVIATION = '5S 219 6. The Flowcharts The Main Program module flowchart: GOSUB INPUT SUBROUTINE GOSUB PROCESS SUBROUTINE GOSUB OUTPUT SUBROUTINE 220 The Input Subroutine flowchart: ENTER CREATE ARRAY Y(50) PRINT "HOW MANY NUMBERS?" INPUT N INPUT NUMBER Y(I) RETURN The Processing Subroutine flowchart: ENTER LET SUM = SUM + LET SUMSQR LET SUMSQR ET S=SQR (SUMSQR/N) ( - (MEAN**2) ) SPECTRUM FORMULA USES 7, NOT **, RETURN 222 The Output Subroutine flowchart: ENTER PRINT MEAN PRINT "STANDARD DEVIATION=" PRINT RETURN 223 7. The Program ед The Мат Program Моаше REM "SDEVIATIDN" FEM 339 9 3 3 9 ЗЕ ЗЕ ЗЕ C 3 9€ 93639963 жҰМАТМ FROGRAM MOLD жж REM **INFLUT DATA жж GOSUE 100 REM **CALCILATE* GOSUE zoo REM ##FRINT RESLULTS3* BOSE 400 = TOF КЕМ **ENI! MAIN жж 5 ы ЭЕ ЗЕ ЗЕ ЗЕ ЭЕ 7.2 The Input Subroutine Module 95 100 110 120 130 140 SQ 160 170 120 190 КЕМ жж А ЗЕ ЭЕ ЭЕ ЭЕ ЖЕ Ж X*INFUT SUBROUTINE жж DIM Y(S05 FRINT “HOW MANY NLMEEFRZ?'": INFLIT N FRINT N FOR Ізі ТОМ INPUT YLI) PRINT ҮСІЗ;" "3 NEXT I RETURN REM *#*#END INFUT SUE жж аз 7.3 The Calculation Module 200 210 220 220 240 220 260 270 290 290) 300 210 —O FEM 339 3 € € 3C 9€ 9€ 9€ 9€ 9€ 3€ 303030 3E 3E HE XxCOLCULATION SUE жж SUM=0 FOR Ісі ТОМ LET SUM=SUM+Y C1) NEXT I LET MEAN=SUIM/N LET СИМЕПК-О0 ЕПЕ Ісі TON LET ФШИМЕОПЕ-СИМФОЕ-һ (Y (I) X 2 NEXT I LET $= Sik (MEAN жж ЕЕТМЕМ LET [ ^ Spectrum] 2⁄2 ССӘПМЕШЕ/М2- 29) FEM **END CALC ‘Sue мен JC 3 3C 3C 30 3636 Ж 9C EE EE 7.4 The Output Module 400 REM 33939 9c X X 3€ 9€ 3C € 9€ 9€ 3€ EHH #*H0UTFUT SUBROUTINE жж 410 PRINT 420 FRINT "МЕАМ-“?МЕАМ 430 PRINT 224 440 PRINT “STANDARD DEVIATION 450 RETURN 460 REM **END OUTPUT SUB жж 333€ CICERO JEDE E EXER ЭН 8. Documentation 1) This program will compute and print the Mean and Standard Deviation of a collection of data items (numbers). 2) It allows for a maximum of 50 items to be entered. You can increase the size of array Y if you wish to deal with more data. 3) The numbers can be of any size, positive or negative, to the limit of the computer's handling capacity. This is large — you will not exceed it. 4) To run the program key in RUN, and enter numbers one at a time, presing NEWLINE (ENTER) after each one has been keyed in. Sample run to find Mean and Standard Deviation of 30, 31, 22, 5, бу 7, 30, 12. 22, 3: HOW MANY NUMBERS ? 10 20 31 325 6 7 10113 27 5 MEAN = 16.4 STANDARD DEVIATION = 11.45603 Exercise The example program to compute and print the standard deviation of a set of data items does not include a pseudocode description of the algorithm, and the documentation process is incomplete in other ways too. i 2, Complete the programming procedure by doing the following: Write out a pseudocode description of the algorithm. Perform a pre-coding walk through, checking the values of the variables, counters and expressions for each subroutine module. Key in the program and debug it. Insert breakpoints in each subroutine and perform a program trace. Insert PRINT statements to print out values of variables, counters and expressions. Obtain a program listing from the printer and run the program for a sample set of data. Keep a copy of the printer output. Document the program fully in your notebook. 225 SECTION P: THE CHARACTER SET AND CODES Pi: The ZX81 Character Set and Codes CODE/CHR$ CODE/CHR$ Ü - K] 49 L 1 F] 50 M E ГЛ 51 N 3 = 52 O 4 kl 53 P 5 D 55 r0 от 55 R 7 P 56 S o B 57 ў 9 ШЫ 58 U uw m 59 V 11 n 60 W 12 £ 61 x 13 $ 62 Y 14 : 63 2 15 ? 64 RND 16 ( 65 INKEY£ 17 66 PI 18 67 19 68 20 - 69 21 4 70 22 = 71 23 * 79 24 / 73 95 74 МОТ 26 75 USED 27 | 76 28 0 77 29 1 78 30 2 79 31 2 80 32 + 81 33 5 82 34 6 83 35 7 84 36 8 85 37 9 86 38 A 87 39 B 88 40) С 89 41 D 90 42 E 91 43 F 99 44 * 93 45 H 94 46 I 95 47 J 96 48 K 97 226 CODE/CHR$ 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 NOT USED + Å <> GRAPHICS EDIT NEW LINE (ENTE RUBOUT (DELET K/L Mode FUNCTION NOT USED NUMBER CURSOR БЕЙБЫТ” лы | ТЫШ inverse `` Inverse £ Inverse $ Inverse : Inverse ? Inverse ( inverse ) inverse > CODE/CHR$ 147 inverse < 148 inverse = 149 inverse + 150 inverse — 151 inverse * 152 inverse / 153 inverse ; 154 inverse , 155 inverse . 156 inverse 0 157 inverse 1 158 inverse 2 159 inverse 3 160 inverse 4 161 inverse 5 162 inverse 6 163 inverse 7 164 inverse 8 165 inverse 9 166 inverse À 167 inverse B 168 inverse C 169 inverse D 170 inverse E 171 inverse F 172 inverse G 173 inverse H 174 inverse I 175 inverse J 176 inverse K 177 inverse L 178 inverse M 179 inverse N 180 inverse O 181 inverse P 182 inverse О 183 inverse R 184 inverse S 185 inverse T 186 inverse U 187 inverse V 188 inverse W 189 inverse X 190 inverse Y 191 inverse Z 192 тар 193 АТ 194 ТАВ 195 (МОТ USED) 196 CODE 197 VAL 198 LEN 199 SIN 200 COS 201 TAN 202 ASN CODE/CHR$ 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 227 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 ACS ATN LN EXP INT SOR SGN ABS PEEK USR STR$ CHR$ NOT жж OR AND < = > = <> THEN TO STEP LPRINT LLIST STOP SLOW FAST NEW SCROLL CONT DIM REM FOR GOTO GOSUB INPUT LOAD LIST LET PAUSE NEXT PI PRINT PLOT RUN SAVE RAND IF CLS UNPLOT CLEAR RETURN COPY Of the non-printing characters, those that are used, but print a question mark, are the following: 116-121 inclusive 126-127 Inclusive (NOTE: 5 1s the question mark.) 192 is the Quote image character, which prints a single quote. The character set is coded with the numbers 0 to 255. This, you may recall, is the number of values held in a single byte. The characters can thus be accessed with a single byte identification code. This is also the reason why some codes are listed, but have no character associated with them. The same is true of the Spectrum character set, which follows. P2: Spectrum Character Set and Codes Code Character Code Character Code Character 0 35 ж 70 Е 1 36 $ 71 G 2 37 % 72 H 3 not used 38 & 73 I 4 39 | 74 Ј 5 40 ( 75 K 6 PRINT comma 41 ) 76 ІР 7 EDIT 42 it M 8 cursor left 43 + 78 N 9 cursor right +} ; 79 О 10 cursor down 45 — (minus sign) 80 P 11 cursor up 46 ; 81 о 19 DELETE 47 / 82 R 13 ENTER 48 0 83 5 14 number 49 1 84 d 15 not used 50 2 85 U 16 INK control 51 3 86 V 17 PAPER control 52 4 87 W 18 FLASH control 53 5 88 x 19 BRIGHT control 54 6 89 Y 20 INVERSE control 55 7 90 Ж 21 OVER control 56 8 91 [ 22 AT control 57 9 92 / 23 TAB control 58 : 93 ] 24 59 š 94 f 25 60 < 95 aa 26 61 = 96 £ 27 not used 62 > 97 a 28 63 ? 98 b 29 64 @ 99 C 30 65 A 100 d 31 66 B 101 e 52 space 67 C 102 f 33 ! 68 D 103 g 34 69 Е 104 h 228 Code Character Code Character 105 i 159 (p) 213 MERGE 106 j 160 (q) 214 VERIFY 107 k 161 (r) 215 BEEP 108 l 162 (s) 216 CIRCLE 109 m 163 (t) 217 INK 110 n 164 (u) 218 PAPER 111 о 165 RND 219 FLASH 112 p 166 INKEY$ 220 BRIGHT 113 q 167 PI 221 INVERSE 114 r 168 FN 222 OVER 115 S 169 POINT 223 OUT 116 t 170 SCREENS 994 LPRINT 117 u 171 ATTR 295 LLIST 118 у 172 АТ 226 STOP 119 w 173 TAB 227 READ 120 x 174 VAL$ 228 DATA 121 y 175 CODE 229 RESTORE 122 2 176 VAL 230 NEW 123 { 177 LEN 231 BORDER 124 | 178 SIN 232 CONTINUE 125 } 179 COS 233 DIM 126 ~ 180 TAN 234 REM 127 © 181 ASN 235 FOR 128 т 182 ACS 236 GO TO 129 а 183 ATN 237 GO SUB 130 P| 184 LN 238 INPUT 131 = 185 EXP 239 LOAD 132 n 186 INT 240 LIST 133 e 187 SOR 241 LET 134 a, 188 SGN 242 PAUSE 155 ШТ 189 ABS 243 NEXT 136 m 190 PEEK 244 POKE 137 =" 191 IN 245 PRINT 138 B 192 USR 246 PLOT 139 p 193 STR$ 247 RUN 140 == 194 CHR$ 248 SAVE 141 all 195 NOT 249 RANDOMIZE 142 L. 196 BIN 250 IF 143 Kj 197 OR 251 CLS 144 (a) 198 AND 252 DRAW 145 (b) 199 = 253 CLEAR 146 (c) 200 = 254 RETURN 147 (d) 201 <> 255 COPY 148 (e) 202 LINE 149 (0) 203 THEN 150 (g) 204 ТО 151 (Һ) 205 STEP 152 (i) 206 DEF FN 153 (j) 207 CAT 154 (k) { user 208 FORMAT 155 (1) ( graphics 209 MOVE 156 (m) 210 ERASE 157 (n) 211 OPEN # 158 (o) 212 OPEN # 229 There is an important point to be noted with regard to the Spectrum character set, which does not apply to the ZX81. Among the Spectrum character set, codes 16 to 23 are control characters which are used to specify certain attributes of the character cell for printing purposes. These require arguments within a certain range (0 to 9 for colours, or 0 and 1 for on or off, etc.). Codes 6 to 14, 22 and 23 are also control characters for printing and editing. The problem with using CHR$ with these control characters is that they can be used in programs, and are then called by inserting, e.g. CHR$ 20, followed by the argument. This means that a simple call to PRINT one of these CHRS will cause the computer to think it is being given an instruction, and the syntax demands an argument. If this is not forthcoming after the CHR$, or the argument is in the wrong range, an error message results when the Spectrum cannot do what it thinks it is being asked to do. Some of these control characters, however, for colour (dealt with in Section W), and also for print control can be usefully placed in programs. If we take CODE 8, which is a cursor control character, we can write a program like this: 10 PRINT ‘‘SIN”’; 20 PAUSE 50 30 PRINT CHR$ 8;CHR$ 8; “АСКЕПр” The CHRS 8 instructions in line 30 backspace the cursor twice, re- setting the PRINT position, so that “АСКЕР” overprints “ТМ”, The upshot of this is that we cannot print out the character set of the Spectrum completely, but must start from CODE 24, after the control characters. This is no great loss, since they print (or would print, if you could get them to!) either a space or a question mark. Remember these control characters, though, as they can sometimes be useful in a program, although mostly it is far more convenient to use the BASIC instructions. For example, we can use CHR$ 23 instead of TAB: 10 PRINT CHR$ 23;10; “ТАВ CONTROL" This is not an advantage over using TAB! However it does show how these characters are used by the computer- it inserts them into program listings where the control function (e.g. T'AB), has been used. TAB itself does not have a control function, and needs CHR$ 23 placed after it to work. P3: Characters The ZX81 and Spectrum have a character alphabet consisting of 256 items which include numeric characters, alphabetic characters, keywords, instructions, commands, operators, graphics and inverse graphics symbols and other symbols. As 230 seen in the tables in the previous Units, of these 256 items some are not used at all, and some are non-printing (i.e. control characters). In Appendix III the ZX81 character codes are laid out by character type and their position on the keyboard. Spectrum codes are referenced alphabetically in Unit W1. The CODE (occupying a single byte) identifies each character uniquely for input/output purposes – i.e. input from the keyboard and output to the screen or printer. The ZX81 has a non-standard character set unique to the machine. The Spectrum has a character set in which the characters used have the codes of the ASCII character set (an internationally agreed standard) for the most part. Non-standard ASCII characters are the symbols for £ and ©, and the graphics characters. Р4: CHR$ and Code The purpose of the instructions CODE and CHR is to convert from the code to the character and vice versa. The ZX81 and Spectrum have different character sets and codes, but the instructions work in the same way. CODE CODE is a function that takes a character or string and gives as a result the numeric code that the character (a single letter string, or first character in a string) cor- responds to. For example: CODE S gives 56 on the ZX81, 83 on the Spectrum CODE “ABCD” gives CODE А, 38 on the ZX81, 65 on the Spectrum CODE X$ gives the code of the first (or only) character in X$ CODE D$(3) gives the code of the third character in D$. CHR$ CHR$ (N), where N is a numeric expression with a value 0 < = N < = 255, is a function that gives as a result the single character whose code is N. CHR$ does the opposite of CODE. For example: CHRS (A + B + C) CHRS$ (X/Z) CHR$ (INT(RND * 255)) CHR$ 36 gives 8 on the ZX81, $ on the Spectrum 231 To see the inverse relationship of CHR$ and CODE, key in the following as direct commands: PRINT CHR$ 50 will print M on the ZX81, 2 on the Spectrum PRIN T CODE 52" ° will print 30 on the ZX81, 50 on the Spectrum PRINT CODE CHR$ 50 will print 50 PRINT CODE “A” will print 38 on the ZX81, 65 on the Spectrum PRINT CHR$ 38 will print A on the ZX81, & on the Spectrum PRINT CHR$ CODE “А” will print A The next program will print out all the characters used on the ZX81. 10 FOR Е=0 TO 255 20 SCROLL 20 PRINT Е, CHR F 40 NEXT F For the Spectrum, as noted above, we must miss out some CHR$ and line 20. Line 10 must read FOR F = 24 TO 255. Key it in and run it. Add: 3:9 LPRINT F; TAE à: CHF F to get a printer listing. A better program (since it uses less printer paper!) but one with an expression you won't understand until we cover logic, is this one: 10 REM ##CHARACTER ЕТЖ 20 LFRINT "CODE/CHE$": TAB 10; "CODE/ICHR$":; TAB zZO:"CODE/CHRE$" 30 FOR Е=0 To 85 40 LFRINT F? ТАЕ 4; CHES F; ТАБ 10;F+sé; TAE 14; CHES$ CF+ie); ТАЕ 20% (F+172 AND F+172<25693; TAE 24; CHES (F+17Z AND Е+172<256) ou NEXT F Use these lines for the Spectrum version: 20 FOR Ғ-24 To 77 40 LPEINT F; TAE 4; CHES F; TAE 10:F*77: ТАР 14: CHES (Е%773; TAB 20:Е+154; TAE 24: CHES (F+154) Exercises 1 Key in and run the following programs. You may find some surprising results, due to the control characters, on the 232 Spectrum. No harm will be done. (a) 10 FOR F = 0 TO 255 (Spectrum: FOR Е = 24 ТО 255) 20 PRINT CHRS F; 30 NEXT F Notice that the word characters print with the spaces that your computer automatically inserts in program lines. (b 10 RAND 20 PRINT CHR$ INT (128* RND + 128) 30 GOTO 20 (c) 10 INPUT A$ 20 PRINT A$, CODE A$ 30 GOTO 10 (d) 10 PRINT “INPUT STRING OF 6 CHARACTERS" 20 INPUT A$ 30 FOR F =1 TO 6 40 PRINT A$(F), CODE АЖЕ) 50 NEXT F (e) 10 RAND 20IF INT (RND*2)=1 THEN PRINT CHR$ INT (RND*128) 30 IF INT (RND*2)-0 THEN PRINT CHR$ (INT(RND*128) + 128) 40 GOTO 20 (f 10 RAND 20 LET A$ = CHR$ INT (RND* 255) 30 SCROLL 40 PRINT CODE A$, A$ 50 GOTO 20 In this last program, Spectrum owners can omit line 30 and simply respond to the Scroll? prompt by pressing ENTER. Write a program that given a number (code), will check that 0 < = code < = 255, and will print out the character. On the Spectrum, the program should print “CONTROL CHARACTER” if the CODE is between 6 and 23. Write a program that when given an alphabetic character as an input will print out the next in the alphabet. If the character input was ‘Z’ then ‘A’ should be printed. SECTION О: GRAPHICS Q1: More Printing Since we dealt with the PRINT instructions, you have been introduced to other statements that can be used with the PRINT statements for format and manipulation. Loops are of use in printing. For instance we can set up an empty string with 32 spaces and use it to clear different areas: 20 LET A$ = ‘‘(32 врасев)” ЖІТІ ӘЛГІ 100 FOR Х-11 ТО 21 110 PRINT АТ X, 0; A$ 120 NEXT X will clear the bottom half of the screen, and we could use it repeatedly, as a subroutine, if we wished. We then avoid using CLS, which would mean re-printing anything that we wanted to keep on the screen. Except for numbers, anything we wish to print must be in the form of a string, either between quotes, a string variable, part of a string array, or a CHR$(X) instruction. Obviously any operations or functions used with strings may be useful, and in the same way as: 10 PRINT (1 + 3) prints 4, we can use: 20 PRINT A$ (X TO Y) to extract the desired characters of A$. Enter and run this program 10 LET A$-"ABRACADAEEA" 20 LET L= LEN ñ$ 30 FOR X=1 TO 6 40 PRINT TAE 10+X;ASCX ТО Lela}? 20 NEXT X Remember that numbers can always be treated as strings, and vice versa, using VAL and STR$. This is often useful for formatting numbers. For example, with a number X, this program: 234 10 LET A$="0000" 20 LET BS= STRS X ЗО FOR F-1 Tü 4 40 IF LEN B$4F THEN GOTO 70 20 LET A$(CFD-E$CF? &O NEXT F 70 PRINT A$ will print (һе first four digits of any number, ог follow (һе number with zeros if less than 4 digits. Change the zeros to spaces, and you have a number string that will overprint any other string however many digits are in the original. Code the program in with A$ = (4 spaces)’ and try it. As it is, you wil have to enter X as a direct command (LET Х= 123, then NEWLINE/ENTER) and then use GOTO 10, since RUN would clear the variables (in this case, the value of X you have just entered). This principle can be expanded. Here is an example of a subroutine used to justify numbers and print them in the position required for the decimal places to be in the same column: 10 REM "FORMAT" 20 REM *FORMAT SUBROUTINE For *NUMEERS ж 30 REM #COLUMN NUMBER ЕСЕ + *#DECTMAL РАСЕ + 40 LET t=12 S0 REM *INITIALISE GOSUB* ео LET ҒОЕМАТ-УООО 70 REM *NUMBER* во INPUT М1 7O REM #*#INITIALIZE NUMEER* 100 LET N=N1 110 GOSUE FORMAT 200 REM *MORE NUMBERS + 210 FOR ісі TQ 4