On the number of iterations required by Von Neumann addition

We investigate the number of iterations needed by an addition algorithm due to Burks et al. if the input is random. Several authors have obtained resu lts on the average case behaviour, mainly using analytic techniques based o n generating functions. Here we take a more probabilistic view which leads to a limit theorem for the distribution of the random number of steps requi red by the algorithm and also helps to explain the limiting logarithmic per iodicity as a simple discretization phenomenon.