In the previous chapter we explored a few ways that numbers can be represented in a digital computer, but we only brieﬂy touched upon arithmetic operations that can be performed on those numbers. In this chapter we cover four basic arithmetic operations: addition, subtraction, multiplication, and division. We begin by describing how these four operations can be performed on ﬁxed point numbers, and continue with a description of how these four operations can be performed on ﬂoating point numbers.
Some of the largest problems, such as weather calculations, quantum mechanical simulations, and land-use modeling, tax the abilities of even today’s largest computers. Thus the topic of high-performance arithmetic is also important. We conclude the chapter with an introduction to some of the algorithms and techniques used in speeding arithmetic operations.