Cybernetics And Systems Analysis logo
Editorial Board Announcements Abstracts Authors Archive
Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 681.04
V.A. Krasnobayev1, A.A. Kuznetsov2, S.A. Koshman3, K.O. Kuznetsovа4


1 V.N. Karazin Kharkiv National University, Kharkiv, Ukraine

v.a.krasnobaev@gmail.com

2 V.N. Karazin Kharkiv National University, Kharkiv, Ukraine

kuznetsov@karazin.ua

3 V.N. Karazin Kharkiv National University, Kharkiv, Ukraine

s_koshman@ukr.net

4 V.N. Karazin Kharkiv National University, Kharkiv, Ukraine

kate7smith12@gmail.com

A METHOD FOR IMPLEMENTING THE OPERATION OF MODULO ADDITION
OF TWO NUMBERS RESIDUES OF THE RESIDUAL NUMBER SYSTEM

Abstract. The paper describes a method for implementing the arithmetic operation of modulo mi addition of the residues of two numbers in the residual number system (RNS). The method is based on the use of modulo M = 2n –1 adders, which consist of a set of sequential binary single-digit adders, by introducing and using additional feedbacks. The authors formulate the rules for introducing additional feedbacks, which makes it possible to implement the addition operation for an arbitrary modulo of RNS. Examples of the synthesis of binary adders and examples of the operation of RNS modulo addition of two numbers residues are given.

Keywords: computer system, residual number system, small-bit binary adder, positional number system, modular addition operation.



FULL TEXT

REFERENCES

  1. Akushsky I.Ya., Yuditsky D.I. Machine arithmetic in residual classes. Moscow: Sov. radio, 1968. 440 p.

  2. Specialized computer technologies in computer science [in Ukrainian]. ed. Y.M. Nykolaychuk. Ternopil: Terno-graf LLC, 2017. 913 p.

  3. Kornilov A.I., Semenov M.Yu., Kalashnikov V.S. Methods for hardware optimization of adders for two operands in the residual class system. Izv. vuzov. Electronics. 2004. N 1. P. 75–82.

  4. Bayoumi M.A., Jullien G.A., Miller W.C. A VLSI implementation of residue. Adders IEEE Trans. on Circuits and Systems. 1987. Vol. 34, N 3. P. 284–288.

  5. Kornilov A.I., Isaeva T.Yu., Semenov M.Yu. Methods for logical synthesis of adders with fast transfer modulo (2n - 1) based on BDD technology. Izv. vuzov. Electronics. 2004. N 3. P. 54-60.

  6. Dolgov A.I. Diagnostics of devices operating in the residual class system. Moscow: Radio i svyaz', 1982. 64 p.

  7. Safari A., Nugent J., Kong Y. Novel implementation of full adder based scaling in residue number systems. 2013 IEEE 56th International Midwest Symposium on Circuits and Systems (MWSCAS). 4–7 Aug. 2013. Columbus, OH, 2013. P. 657–660. doi: 10.1109/MWSCAS.2013.6674734.

  8. Shugang Wei. Fast signed-digit arithmetic circuits for residue number systems. IEEE International Conference on Electronics, Circuits, and Systems (ICECS). 6–9 Dec. 2015. P. 344–347.

  9. Ananda Mohan P.V. Residue number systems: Theory and applications. Birkhuser; Basel: Springer International Publishing, Switzerland, 2016. 351 p.

  10. Balaka E.S., Telpukhov D.V., Osinin I.P., Gorodetsky D.A. Comparative research and analysis of methods of hardware implementation of modular adders. Universum: Engineering Sciences. 2016. N 1 (23). URL: https://cyberleninka.ru/article/n/sravnitelnoe-issledovanie-i-analiz -metodov-apparatnoy-realizatsii-summatorov-po-modulyu.

  11. Gorbenko I., Hanzia R. Examination and implementation of the fast method for computing the order of elliptic curve. European Journal of Enterprise Technologies. 2017. Vol. 2, N 9 (86). P. 11–21.

  12. Krasnobayev V.A., Koshman S.A. Method for implementing the arithmetic operation of addition in residue number system based on the use of the principle of circular shift. Cybernetics and Systems Analysis. 2019. Vol. 55, N 4. P. 692–698. https://doi.org/10.1007/s10559-019-00179-8.
© 2020 Kibernetika.org. All rights reserved.