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Issue RAIRO-Theor. Inf. Appl.
Volume 35, Number 2, March-April 2001
Page(s) 187 - 206
DOI 10.1051/ita:2001115

DOI: 10.1051/ita:2001115


Theoret. Informatics Appl. 35, 187-206 (2001)

On the number of iterations required by Von Neumann addition

Rudolf Grübel1 and Anke Reimers2

1  Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, 30060 Hannover, Germany; (rgrubel@stochastik.uni-hannover.de)
2  Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, 30060 Hannover, Germany;

Abstract
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.


AMS Subject: 68Q25, 65Y20.

Key words: Carry propagation -- limit distributions -- total variation distance -- logarithmic periodicity -- Gumbel distributions -- discretization -- large deviations.


© EDP Sciences 2001


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