Floating-point number representations: base choice versus exponent range
Paul L. Richman · 1967
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 we find that $\Beta$ = 2 is always best. However the analysis is done to cover all cases.