An approximate and empirical study of the distribution of adder inputs and maximum carry length propagation

Abstract

This paper investigates, using sampled data, the commonly used hypothesis that integer operands reaching the adder of a computer are uniformly distributed. Questions raised on the validity of that hypothesis are reinforced and their impact on the calculation of the average of the worst case length of carry propagation is considered. An approximate formula is developed for the worst case carry chain length when the arithmetic operands are restricted in magnitude.