Computer arithmetic is a field of computer science that investigates how computers should represent numbers and perform operations on them. It includes integer arithmetic, fixed-point arithmetic, and the arithmetic this book focuses on: floating-point (FP) arithmetic, which will be more thoroughly described in Chapter 1. For now, let us say that it is the common way computers approximate real numbers and that it is described in the IEEE-754 standard [IEE 08]. As in scientific notations, numbers are represented using an exponent and a significand, except that this significand has to fit on a certain amount of bits. As this number of bits (called precision) is limited, each operation may be inexact due to the rounding. This makes computer arithmetic sometimes inaccurate: the result of a long computation may be far from the mathematical result that would have been obtained if all the computations were correct. This also makes computer arithmetic unintuitive: for instance, the FP addition is not always associative.
source: Computer Arithmetic - an overview | ScienceDirect Topics
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