Further Reading

A brief account of early mathematics in Western civilization can be found in Bunt (1988).

Knuth (1998) presents a delightful and thorough discussion of the evolution of number systems and computer arithmetic in Volume 2 of his series on computer algorithms. (Every computer scientist should own a set of the Knuth books.)

A definitive account of floating-point arithmetic can be found in Goldberg (1991). Schwartz et al. (1999) describe how the IBM System/390 performs floating-point operations in both the older form and the IEEE standard. Soderquist and Leeser (1996) provide an excellent and detailed discussion of the problems surrounding floating-point division and square roots.

Detailed information about Unicode can be found at the Unicode Consortium Web site, www.unicode.org, as well as in The Unicode Standard, Version 3.0 (2000). The International Standards Organization Web site can be found at www.iso.ch. You will be amazed at the span of influence of this group. A similar trove of information can be found at the American National Standards Institute Web site: www.ansi.org.

The best information pertinent to data encoding for data storage can be found in electrical engineering books. They offer some fascinating information regarding the behavior of physical media, and how this behavior is leveraged by various coding methods. We found the Mee and Daniel (1988) book particularly helpful.

After you have mastered the ideas presented in Chapter 3, you will enjoy reading Arazi's book (1988). This well-written book shows how error detection and correction is achieved using simple digital circuits. The appendix of this book gives a remarkably lucid discussion of the Galois field arithmetic that is used in Reed-Soloman codes.

If you'd prefer a rigorous and exhaustive study of error-correction theory, Pretzel's (1992) book is an excellent place to start. The text is accessible, wellwritten, and thorough.

Detailed discussions of Galois fields can be found in the (inexpensive!) books by Artin (1998) and Warner (1990). Warner's much larger book is a clearly written and comprehensive introduction to the concepts of abstract algebra. A study of abstract algebra will be helpful to you should you delve into the study of mathematical cryptography, a fast-growing area of interest in computer science.