On the number of iterations required by Von Neumann addition
Institut für Mathematische Stochastik,
Postfach 60 09, 30060 Hannover, Germany;
2 Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, 30060 Hannover, Germany
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 results on the average case behaviour, mainly using analytic techniques based on generating functions. Here we take a more probabilistic view which leads to a limit theorem for the distribution of the random number of steps required by the algorithm and also helps to explain the limiting logarithmic periodicity as a simple discretization phenomenon.
Mathematics Subject Classification: 68Q25 / 65Y20
Key words: Carry propagation / limit distributions / total variation distance / logarithmic periodicity / Gumbel distributions / discretization / large deviations.
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