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On the number of iterations required by Von Neumann addition

Published online by Cambridge University Press:  15 April 2002

Rudolf Grübel  and
Anke Reimers
Rudolf Grübel
Affiliation:
Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, 30060 Hannover, Germany; ([email protected])
Anke Reimers
Affiliation:
Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, 30060 Hannover, Germany
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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.

Keywords

Carry propagationlimit distributionstotal variation distancelogarithmic periodicityGumbel distributionsdiscretizationlarge deviations.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 2 , March 2001 , pp. 187 - 206
Copyright
© EDP Sciences, 2001

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