ABSTRACT
The speed of a computer is determined to a first order by the speed of the arithmetic unit and the speed of the memory. Although the speed of both units depends directly on the implementation technology, arithmetic unit speed also depends strongly on the logic design. This chapter describes algorithms for floating-point arithmetic. Regarding notation, capital letters represent digital numbers, while subscripted lowercase letters represent bits of the corresponding word. Much arithmetic is performed with fixed-point numbers, which have constant scaling. The numbers can be interpreted as fractions, integers, or mixed numbers, depending on the application. There are two types of division algorithms in common use: digit recurrence and convergence methods. The digit recurrence approach computes the quotient on a digit-by-digit basis; hence, they have a delay proportional to the precision of the quotient. The main advantage of floating-point arithmetic is that its wide dynamic range virtually eliminates overflow and underflow for most applications.
