The Determination of Carry Propagation Length for Binary Addition

It is well known that the expected maximum length of nonzero carry propagation in the addition of two uniformly distributed binary numbers of n-digits each is less than log2 n. The propagation of both zero and nonzero carry is required in the employment of asynchronous self-timing addition. For the addition of two n-digit binary numbers which are uniformly distributed, a simple recursive algorithm is readily derived for the exact determination of the expected maximum length of zero or nonzero carry propagation.