The Definitive Guide to How Computers Do Math : Featuring the Virtual DIY Calculator

441 Pages·2005·2.468 MB·English

by  Clive Maxfield, Alvin Brown

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THE DEFINITIVE GUIDE TO
HOW
COMPUTERS
DO MATH
Featuring
The Virtual DIY Calculator
Clive “MAX” Maxfield
Alvin Brown
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1 A JOHN WILEY & SONS, INC., PUBLICATION
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Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any
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except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without
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MA 01923, [phone], fax [phone], or on the web at www.copyright.com. Requests to
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Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best
efforts in preparing this book, they make no representations or warranties with respect to the
accuracy or completeness of the contents of this book and specifically disclaim any implied
warranties of merchantability or fitness for a particular purpose. No warranty may be created or
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herein may not be suitable for your situation. You should consult with a professional where
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Wiley also publishes its books in a variety of electronic formats. Some content that appears in print,
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Library of Congress Cataloging-in-Publication Data is available.
ISBN-13 978-0471-73278-5
ISBN-10 0-471-73278-8
Printed in the United States of America.
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To all our friends
who make the world
such a wonderful place!
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Contents
Laboratories ix
Do You Speak Martian? xi
Chapter 0 Why This Book Is So Cool 1
This is where we discover just why this book is so cool, and
also why this chapter is numbered “0.”
Chapter 1 Introducing Binary and Hexadecimal Numbers 7
In this chapter we introduce the concepts of the binary and
hexadecimal number systems (but in a much more interesting
manner than most computer books).
Chapter 2 Computers and Calculators 23
Here we rampage through the insides of a simple computer
and calculator, and we also meet our virtual DIY Calculator.
Chapter 3 Subroutines and Other Stuff 35
In this smorgasbord of a chapter, we first discuss logical, shift,
and rotate instructions; then we plunge headfirst into the
stack, subroutines, recursion, and the concept of self-
modifying code.
Chapter 4 Integer Arithmetic 69
This is where we learn the concepts of signed and unsigned
binary arithmetic, and multibyte data representations. In the
labs associated with this chapter we create some integer-based
math subroutines for use in Chapter 5.
Chapter 5 Creating an Integer Calculator 123
This is where things really start to get interesting because we
use the subroutines we developed in Chapter 4 to implement
a simple four-function integer calculator.
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viii CONTENTS
Chapter 6 More Functions and Experiments 135
This may be the last chapter, but turn that frown upside down
into a smile because this is where we discover additional
projects you can undertake, and also how you can compete
with other readers to create better math routines for your
DIY Calculator.
Interactive Laboratories 155–412
This is where you will find the interactive laboratories
associated with Chapters 2 through 5 (see more details
on page ix).
Appendix A Installing Your DIY Calculator 413
In this appendix, we learn how to install the virtual DIY
Calculator presented on the CD-ROM accompanying
this book.
Appendix B Addressing Modes 417
Here we learn about the various addressing modes supported
by the virtual microprocessor powering the DIY Calculator.
Appendix C Instruction Set Summary 429
The tables in this appendix are useful for quickly determining
which instructions are available with which addressing modes.
Appendix D Additional Resources 433
There is a wealth of additional resources for individual
readers and educators on the CD-ROM accompanying the
book and from the DIY Calculator’s website. Also, there are
lots of other really interesting books to read. This appendix
explains it all.
About the Authors 441
Acknowledgments 443
Index 445
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Laboratories
LABS FOR CHAPTER 2: CREATING AND RUNNING PROGRAMS 155
Lab 2a: Creating a Simple Program 157
Lab 2b: Constant Labels and .EQU Directives 169
Lab 2c: Driving the Calculator’s Main Display 173
Lab 2d: Reading from the Calculator’s Keypad 185
Lab 2e: Writing to the Calculator’s Six LEDs 193
Lab 2f: Using the Memory Walker and Other 201
Diagnostic Displays
LABS FOR CHAPTER 3: SUBROUTINES AND OTHER STUFF 219
Lab 3a: Using Logical Instructions, Shifts, and Rotates 221
Lab 3b: Understanding the Program Counter (PC) 237
Lab 3c: Using the Index Register (X) 245
Lab 3d: Using the Stack and Stack Pointer (SP) 255
Lab 3e: Using Subroutines 261
Lab 3f: Using Recursion 267
LABS FOR CHAPTER 4: INTEGER ARITHMETIC 275
Lab 4a: Creating a Testbench Program 277
Lab 4b: Creating a 16-bit ADD Subroutine 299
Lab 4c: Creating a 16-bit SUBTRACT Subroutine 311
Lab 4d: Creating a 16-bit NEGATE Subroutine 317
Lab 4e: Checking for Overflow in the ADD and 323
SUBTRACT Routines
Lab 4f: Creating a 16-bit MULTIPLY Subroutine 333
Lab 4g: Creating a 16-bit DIVIDE Subroutine 351
LABS FOR CHAPTER 5: CREATING AN INTEGER CALCULATOR 373
Lab 5a: Creating the Calculator Framework 375
Lab 5b: Adding Some Low-Level Utility Routines 383
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x LABORATORIES
Lab 5c: Creating a Decimal GETNUM (“get number”) 389
Subroutine
Lab 5d: Creating a Decimal DISPNUM (“display number”) 395
Subroutine
Lab 5e: Implementing a Four-Function Integer Calculator 405
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Do You Speak Martian?
There are an abundance of books on computer architectures, computer
logic, and computer mathematics, and most of these works discuss vari-
ous techniques for representing and manipulating numbers inside com-
puters. Sadly, however, it appears that the majority of these tomes are
written by visitors from the planet Mars, whose keen understanding of
higher mathematics is somewhat offset by their limited grasp of the
English language.
“Say it’s not so!” you cry, but the proof is irrefutable. When was the
last time you waded through a book on computer mathematics without
your brain overheating? Much like reading Being and Nothingness by the
famous French philosopher Jean Paul Sartre, one could mull over many
of these cryptic masterpieces until the end of time without gaining so
much as the faintest clue as to what was in their authors’ minds.
This is why we have been moved to write this modest attempt at in-
troducing the basics of computer arithmetic in words we can all under-
stand. An impossible task, some may say, but we dare to fly in the face of
conventional wisdom. Now, read on. ...
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The Definitive Guide to How Computers Do Math: Featuring the Virtual DIY Calculator.
Clive “MAX” Maxfield and Alvin Brown. Copyright  2005 John Wiley & Sons, Inc.
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CHAPTER
0 WHY THIS BOOK
IS SO COOL
“
The simplest schoolboy is now familiar with
facts for which Archimedes would have
”
sacrificed his life.
ERNESTRENAN(1823–1892) in Souvenirs
D’enfance et de Jeunesse(1887)
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0 ●● The sock color of choice for the discerning
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●● Why this book is so cool
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●● That there are jobs awaiting time-travelers
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0 ●● Some “stuff” about calculators
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