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


The Basics of Computer Arithmetic Made Enjoyable and Accessible-with a Special Program Included for Hands-on Learning

"The combination of this book and its associated virtual computer is fantastic! Experience over the last fifty years has shown me that there's only one way to truly understand how computers work; and that is to learn one computer and its instruction set-no matter how simple or primitive-from the ground up. Once you fully comprehend how that simple computer ...

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The Basics of Computer Arithmetic Made Enjoyable and Accessible-with a Special Program Included for Hands-on Learning

"The combination of this book and its associated virtual computer is fantastic! Experience over the last fifty years has shown me that there's only one way to truly understand how computers work; and that is to learn one computer and its instruction set-no matter how simple or primitive-from the ground up. Once you fully comprehend how that simple computer functions, you can easily extrapolate to more complex machines."
-Fred Hudson, retired engineer/scientist

"This book-along with the virtual DIY Calculator-is an incredibly useful teaching and learning tool. The interesting trivia nuggets keep you turning the pages to see what's next. Students will have so much fun reading the text and performing the labs that they won't even realize they are learning."
-Michael Haghighi, Chairperson of the Business and Computer Information Systems Division, Calhoun Community College, Alabama

"At last, a book that presents an innovative approach to the teaching of computer architecture. Written with authority and verve, witty, superbly illustrated, and enhanced with many laboratory exercises, this book is a must for students and teachers alike."
-Dr. Albert Koelmans, Lecturer in Computer Engineering, University of Newcastle upon Tyne, UK, and the 2003 recipient of the EASIT-Eng. Gold Award for Innovative Teaching in Computer Engineering

Packed with nuggets of information and tidbits of trivia, How Computers Do Math provides an incredibly fun and interesting introduction to the way in which computers perform their magic in general and math in particular. The accompanying CD-ROM contains a virtual computer/calculator called the DIY Calculator, and the book's step-by-step interactive laboratories guide you in the creation of a simple program to run on your DIY Calculator.

How Computers Do Math can be enjoyed by non-technical individuals; students of computer science, electronics engineering, and mathematics; and even practicing engineers. All of the illustrations and interactive laboratories featured in the book are provided on the CD-ROM for use by high school, college, and university educators as lecture notes and handouts.

For online resources and more information please visit the author's website at


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Editorial Reviews

From the Publisher
"I found this book to be a lot of fun, and I think many high school teachers and students would enjoy it too." (Mathematics Teacher, September 2006)

"Clive 'Max' Maxfield and Alvin Brown have written a wonderful book…about the essential workings of computers." (The Embedded Muse, February 22, 2006)

"I have not seen a better description of the stack and related concepts. The authors obviously understand that these concepts are usually confusing to novices, and hence they support the material with good and simple examples." (Computing, January 16, 2006)

"It looks like Max has done it again, i.e., written another technical book that reminds us why we studied electronics in the first place—for the sheer fun of it." (Chip Design Magazine, December 2005/January 2006)

"The book is fun, highly informative, and full of vitally important stuff for both the technical and non-technical alike." (EDA Confidential, November 21, 2005)

"Everybody can learn from this lively book but it [is] especially helpful for teachers and engineers who want to share their interest in math and computing machinery with others." (Wireless Net DesignLine Newsletter, November 10, 2005)

"For those interested in a slightly off-beat approach to learning the basics of computer architectures, Maxfield and Brown have put together a multimedia package that's well worth the price of admission." (Electronic, October 20, 2005)

"The book is perfect for students and those among us who aspire to really understand what is going on in those gismos…the prose is easy to read, and the lab exercises are well designed." (Gabe On

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Product Details

  • ISBN-13: 9780471732785
  • Publisher: Wiley
  • Publication date: 9/9/2005
  • Edition description: BK&CD-ROM
  • Edition number: 1
  • Pages: 464
  • Product dimensions: 7.46 (w) x 9.09 (h) x 0.99 (d)

Meet the Author

CLIVE "MAX" MAXFIELD is a bestselling author and engineer with a large following in the electronic design automation (EDA) and embedded systems industries. He is also one of the founders and President of the high-technology marketing consultancy TechBites (

ALVIN BROWN has spent over thirty years working in the electronics and computing industries. He currently acts as an engineering manager supervising remote development groups around the world.

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Table of Contents


Do You Speak Martian

Chapter 1. Why This Book Is So Cool.

Chapter 2. Introducing Binary and Hexadecimal Numbers.

Chapter 3. Computers and Calculators.

Chapter 4. Subroutines and Other Stuff.

Chapter 5. Creating an Integer Calculator..

Chapter 6. More Functions and Experiments.

Interactive Laboratories.

Appendix A: Installing Your DIY Calculator.

Appendix B: Addressing Modes.

Appendix C: Instruction Set Summary.

Appendix D: Additional Resources.

About the Authors.



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Sort by: Showing all of 3 Customer Reviews
  • Anonymous

    Posted February 27, 2006

    Great Intro to Computing

    The book is aimed at people starting out in computers we experts know this stuff cold. But an interested 15 year old could get truly in-depth insight into the mysteries of computing from this volume. It¿s a very readable book laid out with easy-on-the-eyes formatting and a plethora of clear illustrations. The illustration of a LIFO stack just booms clarity. Chapters start with relevant and often amusing quotes one of my favorites is Lewis Carroll¿s ¿The four branches of arithmetic: ambition, distraction, uglification, and derision.¿ Quickly page through the book and you¿ll be puzzled by its organization. The first 55 pages (out of 450) comprise its ostensible meat. The rest are labs for each chapter, a series of problems the authors pose to illustrate important concepts. They nudge you through the solutions ¿ there are no proofs left to the confused student. The labs are very well-written accessible activities in which the authors take the reader along hand-in-hand. They¿re a bit insidious: work through them and the reader will become a reasonably competent assembly-language programmer, without realizing he¿s learning one of the more difficult aspects of programming. There¿s a perverse genius in covertly slipping assembly language into one¿s head without pain. The authors¿ sure hands guide one along each lab, with descriptions and demonstrations till the code that¿s required is almost anticlimactic: ¿of *course* it must be like this!¿ But how is one to do a lab? You need a computer, right? Well, sure, but the authors provide a DIY Calculator on CD, an interactive and sophisticated bit of code that runs on a PC. It sports the usual display and math functions, plus its own low-level programming language. And, it¿s extensible. The companion website contains plenty of downloadable extension code, plus the calculator itself. Like open source advocates they hope the community will contribute to the set of routines. The web site also has a fabulous background to the field of computing that, if you¿re a computer history buff, will suck you in and surely doom the schedule of whatever product you¿re working on now. Where too many computer books have a dreary chapter about number systems, ¿How Computers Do Math¿ cover the subject in an entertaining and very complete fashion. From basic binary math they go on to show how one constructs an adder out of gates. Signed, unsigned, multiplication, rounding (9 different approaches!), BCD ¿ it¿s all there, and it¿s all extremely comprehensible.

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  • Anonymous

    Posted December 16, 2005

    Clive 'Max' Maxfield's books are for everyone, even the 'old' engineer

    'Max' Maxfield has a very original style that does away with 'you already know this' and goes to 'let's go there together AND have a lot of fun doing it'. This is a MATH book, dealing in how computers do math, and adds the dimension of learning by doing, by adding a 'virtual' calculator you program to do the math. It may be helpful to know some programming and some digital logic, but 'Bebop to the Boolean Boogie', also by 'Max', gets you there. You go from the DIY 'virtual' calculator (residing on your computer) that does NOTHING, and you, with Clive and Alvin as your guides, make it do basic math. Even us 'old' engineers can have a kick start to the memories of how we used to do things, and may still be doing them today. Added bonus: It is not a dry text book approach. You will have fun doing it.

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  • Anonymous

    Posted June 18, 2009

    No text was provided for this review.

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