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On the number of iterations required by Von Neumann addition

Rudolf Grübel; Anke Reimers — 2001

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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.

On the number of iterations required by Von Neumann addition

Rudolf Grübel; Anke Reimers — 2010

RAIRO - Theoretical Informatics and Applications

We investigate the number of iterations needed by an addition algorithm due to Burks 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.

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