Numerical Analysis and Applications

, Volume 6, Issue 1, pp 71–76 | Cite as

Stochastic model of digit transfer in computing

  • L. Ya. Savel’ev
  • S. V. Balakin


This paper describes a stochastic model of digit transfer. The main characteristics of the transfer process are the number of transfers, the number of groups of consecutive transfers, and the maximum number of consecutive transfers. Two binary numbers with a digit transfer form a triplet, and a sequence of these triplets generates a Markov chain. In our model, the above-mentioned characteristics can be described by functionals on trajectories of this chain: the number of events, the number of runs of these events, and the maximum run length. These characteristics can be efficiently used for estimating the computation speed.


summator summation digit transfer stochastic model random sequence Markov chain run functional expectation variance 


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  1. 1.
    Rabaey, J.M., Chandrakasan, A., and Nikolic, B., Digital Integrated Circuits, A Design Perspective, 2nd ed., Englewood Cliffs, NJ: Prentice Hall, 2002.Google Scholar
  2. 2.
    Preet Pa Singh, R., Kumar, P., and Singh, B., Performance Analysis of 32-Bit Array Multiplier with a Carry Save Adder and with aCarry-Look-Ahead Adder, Int. J. Recent Trends Engin., 2009, vol. 2, no. 6, pp. 83–86.Google Scholar
  3. 3.
    Ercegovac, M.D. and Lang, T., Digital Arithmetic, San Francisco: Morgan Daufmann, 2004.Google Scholar
  4. 4.
    Ugryumov, E.P., Tsifrovaya skhemotekhika (Digital Circuit Engineering), St. Petersburg: BKhVPeterburg, 2001.Google Scholar
  5. 5.
    Khmel’nik, S.I., Encoding of Complex Numbers and Vectors. Theory, Hardware, Modeling, in Mathematics in Computers, Lulu, USA, 2006 (ID 560836).Google Scholar
  6. 6.
    Kemeny, G. and Snell, J., FiniteMarkov Chains, New York: Springer, 1960.Google Scholar
  7. 7.
    Bremaud, P., Markov Chains. Gibbs Fields. Monte Carlo Simulations, and Queues, NewYork: Springer, 1998.Google Scholar
  8. 8.
    Savel’ev, L.Ya. and Balakin, S.V., CombinedDistribution of the Number ofUnities and the Number of 1-Runs in the BinaryMarkov Chain, Disk.Mat., 2004, vol. 16, no. 3, pp. 43–62.MathSciNetGoogle Scholar
  9. 9.
    Balakin, S.V., Distribution of the Maximum of the Run Lengths in the Markov Chain, Obosr. Prikl. Prom. Mat., 2010, vol. 17, no. 4, pp. 531/532.Google Scholar
  10. 10.
    Savel’ev. L.Ya. and Balakin, S.V., Combinatorial Calculation of theMoments of Run Characteristics in Triple Markov Chains, Diskr. Mat., 2011, vol. 23, no. 2, pp. 72–88.MathSciNetGoogle Scholar
  11. 11.
    Savel’ev, L.Ya., Long Runs inMarkovChains, Pred. Teoremy Teor. Ver., 1985, vol. 5, pp. 137–144.MathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Sobolev Institute of Mathematics, Siberian BranchRussian Academy of SciencesNovosibirskRussia

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