FLOATING-POINT NUMBER REPRESENTATIONS: BASE CHOICE VERSUS EXPONENT RANGE.

A digital computer whose memory words are composed of r-state devices is considered. The choice of the base, beta, for the internal floating-point numbers on such a computer is discussed. Larger values of beta necessitate the use of more r-state devices for the mantissa, in order to preserve some minimum accuracy, leaving fewer r-state devices for the exponent of beta. As beta increases, the exponent range may increase for a short period, but it must ultimately decrease to zero. Of course, this behavior depends on what definition of accuracy is used. This behavior is analyzed for a recently proposed definition of accuracy which specifies when it is to be said that the set of q-digit base beta floating-point numbers is accurate to p-digits base t. The only case of practical importance today is t 10 and r 2 and in this case beta 2 is always best. However, the analysis is done to cover all cases. Author