CONVERSION OF A MODULAR NUMBER SYSTEM CODE INTO A GENERALIZED POSITION CODE
Abstract
The article is devoted to the problem of constructing an integrated and characteristic base of modular arithmetic. In particular, calculation estimates are obtained for conversion of a modular code (MC) into a code of a generalized positional number system (GPNS) and based on them the sequential and parallel configurations of the appropriate procedure are synthesized. With its modular structure, the developed algorithms are easy to implement. They include subtraction with multiplication by constants used by the modules of the basis. Computational complexity of sequential and parallel implementations of conversion of MC into the GPNS code according to the proposed algorithms is О(k2) and О(k) of modular operations (k is the power of the basis of the number system) respectively.
About the Authors
A. F. Chernyavsky
A. N. Sevchenko Institute of Applied Physics Problems of the Belarusian State University
Belarus
Belarus
Academician, D. Sc. (Engineering), Professor, Head of the Laboratory
A. A. Kolyada
A. N. Sevchenko Institute of Applied Physics Problems of the Belarusian State University
Belarus
Belarus
D. Sc. (Physics and Mathematics), Chief researcher
References
1. Omondi A., Premkumar B. Residue number systems: theory and implementation. Singapore, Imperial College Press, 2007. 311 p. doi.org/10.1142/9781860948671
2. Kalmykov I. A., Lobodin M. V., Zinov’ev A. V., Demorlukova Ia. V. Converter of the modular code into the generalized polyadic number system code in nonstop control systems. Uspekhi sovremennogo estestvoznaniia = Advances in current natural sciences, 2009, no. 4, pp. 41−43 (in Russian).
3. Sousa L., Antao S. MRC – based RNS reverse converters for the four – moduli sets {2<sup>n</sup>+1.2<sup>n</sup>-1.2 <sup>n</sup>,2<sup>2n+1</sup>-1}and {2<sup>n</sup>+1.2<sup>n</sup>-1.2 <sup>n</sup>,2<sup>2n+1</sup>-1}IEEE Transactions on Circuits and Systems II: Express Briefs, 2012, vol. 59, iss. 4, pp. 244–248. doi.org/10.1109/tcsii.2012.2188456
4. Kolyada A. A., Chernyavsky A. F. Integrated characteristic base of modular number systems. Informatika = Informatics, 2013, no. 1, pp. 106–119 (in Russian).
5. Amerbaev V. M., Soloviev R. A., Telpukhov D. V., Balaka E. S. Construction of residue number system reverse onverters with error correction, based on mixed-number system. Neirokomp’iutery: razrabotka, primenenie = Neurocomputers, 2014, no. 9, pp. 30–35 (in Russian).
6. Ananda Mohan P. V. Residue number systems: theory and applications. Basel, Birchauser (mathematics), 2016. 351 p. doi.org/10.1007/978-3-319-41385-3
7. Chernyavsky A. F., Kolyada A. A. Calculation of the integral characteristics of minimally redundant modular code. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2015, vol. 59, no. 6, pp. 40−46 (in Russian).
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