A stochastic model of a~digit transfer by computing
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 4, pp. 417-423.

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This paper describes a stochastic model of the digit transfer. The main characteristics of the transfer process are the number of transfers, a number of groups of consecutive transfers and a 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. They are: the number of events, the number of runs of these events and a maximum run length. These characteristics can be efficiently used for estimation of a computation speed.
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L. Ya. Savelev; S. V. Balakin. A stochastic model of a~digit transfer by computing. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 4, pp. 417-423. http://geodesic.mathdoc.fr/item/SJVM_2012_15_4_a6/

[1] Rabai Zh. M., Chandrakasan A., Nikolich B., “Proektirovanie arifmeticheskikh blokov: Summator”, Tsifrovye integralnye skhemy. Metodologiya proektirovaniya, Per. s angl., 2-e izd., Vilyams, M., 2007

[2] Preet Pa Singh R., Kumar P., Singh B., “Performance analysis of 32-bit array multiplier with a carry save adder and with a carry-look-ahead adder”, International J. of Recent Trends in Engineering, 2:6 (2009), 83–86

[3] Ercegovac M. D., Lang T., Digital Arithmetic, Morgan Daufmann, San Francisco, 2004

[4] Ugryumov E. P., Tsifrovaya skhemotekhnika, BKhV-Peterburg, SPb., 2001

[5] Khmelnik S. I., Kodirovanie kompleksnykh chisel i vektorov. Teoriya, apparatura, modelirovanie, Mathematics in Computers, Israel; Lulu Inc., USA, 2006, (ID 560836)

[6] Kemeni Dzh., Snell Dzh., Konechnye tsepi Markova, Nauka, M., 1978

[7] Bremaud P., Markov Chains. Gibbs Filds. Monte Carlo Simulations, and Queues, Springer, 1998 | MR

[8] Savelev L. Ya., Balakin S. V., “Sovmestnoe raspredelenie chisla edinits i chisla 1-serii v dvoichnoi markovskoi posledovatelnosti”, Diskretnaya matematika, 16:3 (2004), 43–62 | DOI | MR | Zbl

[9] Balakin S. V., “Raspredelenie maksimuma dlin serii v markovskoi tsepi”, Obozrenie prikladnoi i promyshlennoi matematiki, 17:4 (2010), 531–532

[10] Savelev L. Ya., Balakin S. V., “Kombinatornoe vychislenie momentov kharakteristik serii v troichnykh markovskikh posledovatelnostyakh”, Diskretnaya matematika, 23:2 (2011), 76–92 | DOI | MR

[11] Savelev L. Ya., “Dlinnye serii v markovskikh posledovatelnostyakh”, Predelnye teoremy teorii veroyatnostei, 5, 1985, 137–144 | MR