This well-organized text for a course in computer arithmetic at the senior undergraduate or beginning graduate level is divided into seven parts, each comprising four chapters. Each part is intended to occupy one or two lectures. The book has clearly benefited from the author’s experience in teaching this material. It achieves a nice balance among the mathematical development of algorithms and discussion of their implementation.

Each chapter has 15 or more exercises, of varying difficulty and nature, and its own references. I would have liked to see a comprehensive bibliography for the whole book as well, since this could include items that are not specifically referred to in the text.

The first four parts are devoted to number representation, addition and subtraction, multiplication, and division. These are concerned with integer (or at least fixed-point) arithmetic. The next two parts deal with real arithmetic and function evaluation. The final part, “Implementation Topics,” covers some practical engineering aspects.

Part 1 has chapters titled “Numbers and Arithmetic,” “Representing Signed Numbers,” “Redundant Number Systems,” and “Residue Number Systems.” The first begins with a brief history of the Intel division bug, which serves to introduce the significance of computer arithmetic. A second “motivating example” is based on high-order roots and powers. The primary content describes fixed-radix number systems and radix conversion. It is typical of the book that these sections contain many well-chosen examples and diagrams.

The chapter on signed numbers covers the expected material: sign-magnitude, biased, and complemented representations, including the use of signed digits. Redundant number systems are introduced within the discussion of carry propagation. The mathematical basis for carry-free addition is discussed along with its algorithm. Residue number systems are discussed, beginning with the representation and the choice of moduli. The explanation of conversion to and from the binary system includes a good description of the Chinese remainder theorem.

Part 2, on addition and subtraction, begins with the basics of half and full adders, and carry-ripple adders. This motivates the chapter on carry-lookahead adders. The basic idea and its implementation are presented well. This chapter finishes with a short section on VLSI implementation, which gives pointers to further study. Similar sections appear in most chapters. Variations on the carry-lookahead theme are the subject of the next chapter, while Wallace and Dadda trees of carry-save adders are the final addition topics. This provides a natural link to multiplication.

The basic structure of parts 3 and 4 (on multiplication and division) is the same. There are chapters on basic and high-radix multiplication and division. Tree and array multipliers, and special variations (for squaring and multiply-accumulate) complete the multiplication part. The final chapter on division covers Newton-like methods. One of my few criticisms of the book is that the explanation of SRT and digit selection could be more extensive. A student unfamiliar with these topics might have difficulty gaining a full understanding of this important technique.

Part 5 is concerned with real arithmetic, and the floating-point system in particular. The chapter on real-number representation includes a brief section on logarithmic arithmetic, which offers the student a glimpse of alternatives. Other schemes such as Hamada’s “Universal Representation of Real Numbers” or symmetric level-index could also have been mentioned here. Floating-point arithmetic is described using the integer operations. Rounding and normalization are also discussed. Chapter 19 is a short chapter on errors and their control, which covers most of the basics without giving all the details. For a mathematics course on computer arithmetic, this chapter would need expanding. The final chapter on real arithmetic describes continued fraction, multiple precision, and interval arithmetic.

Part 6 covers function evaluation, with chapters on square-rooting, CORDIC algorithms, variations (iterative methods and approximations), and table lookup. Each chapter describes the basic ideas well and provides a sufficient taste of its subject matter to point the interested student to further study. The description of the CORDIC algorithms is more complicated than necessary. Use of an elementary trigonometric identity would simplify some of the formulas substantially. The use of degrees in the introduction to the CORDIC algorithm is also a dubious choice.

The final part has chapters on high-throughput, low-power, and fault-tolerant arithmetic. Each is fairly brief but would serve as an introduction to some of the practical engineering aspects of computer arithmetic.

Overall, Parhami has done an excellent job of presenting the fundamentals of computer arithmetic in a well-balanced, careful, and organized manner. The care taken by the author is borne out by the almost total absence of typos or incorrect cross-references. I would choose this book as a text for a first course in computer arithmetic.