Fixed‐Point Computer Arithmetic

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. Even for an integer adder, speed can vary easily by an order of magnitude, whereas the complexity varies by less than 50%. Much arithmetic is performed with fixed‐point numbers, which have constant scaling (i.e., the position of the binary point is fixed). The numbers can be interpreted as fractions, integers, or mixed numbers, which depends on the application. Pairs of fixed‐point numbers are used to create floating‐point numbers, the subject of another article.