Definitive Guide to How Computers Do Math

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 (www.TechBites.com). 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.

"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 Reviews.com, 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 Design.com, 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 EDA.com)

• Laboratories ixDo You Speak Martian? xiChapter 0 Why This Book is So Cool 1This 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 7In 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 23Here 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 35In 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 selfmodifying code.Chapter 4 Integer Arithmetic 69This 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 123This 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.Chapter 6 More Functions and Experiments 135This 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 155–412This 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 413In this appendix, we learn how to install the virtual DIY Calculator presented on the CD-ROM accompanying this book.Appendix B Addressing Modes 417Here we learn about the various addressing modes supported by the virtual microprocessor powering the DIY Calculator.Appendix C Instruction Set Summary 429The tables in this appendix are useful for quickly determining which instructions are available with which addressing modes.Appendix D Additional Resources 433There 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 441Acknowledgments 443Index 445