AN APPROACH TO COMPARING NUMBER MODULES IN NUMBER SYSTEMS IN RESIDUAL
The paper considers an approach to comparing the number modules represented in the number systems in residual classes (RNS), one of the bases of which is pn = 2k, where k = 2, 3, 4, .... The approach involves the following sequence of actions.
The decrease in number modules |А| and |В| by an and bn, respectively, where an = rest|А| mod pn and bn = rest|B| mod pn. Next, access to the computer memory at the addresses (a1, a2, . . ., an-1) and (b1, b2, . . . ., bn-1) and selection from the memory the high digits (without k low digits) of the modules |А| and |В| represented in the positional binary system by comparing the selected high digits of the modules. In this case, a larger module will correspond to larger high digits. If the high digits of the modules are equal then the lower digits are compared which coincide with the residues an and bn. In this case, the largest of the lower digits will correspond to the larger module. With this approach, the memory required to store the compared modules when they are written in the positional binary number system is reduced by 2k times, and the word length of the stored words decreases by k binary digits. In addition, the low bit depth of the RNS bases allows the using of tabular calculation methods which increases the speed of calculations.
Thus the proposed approach has a practical orientation and may be of interest to computer developers.
 Tomczak, T. 2008. Fast sign detection for rns (2n–1,2n, 2n+1). IEEE Trans. on Circuits and Systems-I: Regular papers, 55(6): 1502–1511.
 Chervyakov, N. I. and Averbukh, V. M. 2012. Approximated method of non-modular procedures in RNS. Basic researches, 6: 189 – 193.
 Mytsko, E. A. and Mal'chukov, A. N. 2013. Study into hardware implementation of spreadsheet and matrix algorithm of CRC 32 computing. Izv. Tomsk Polytechnic University, 322(5): 182 – 186.
 Anikueva, O. V., Lyalhov, P. A. and Chervyakov. N.I. 2014. Implementation of discrete wavelet transformation in RNS of special type. Infokommunikatsionnye Tekhnologii, 12(4): 4 – 9.
 Magomedov, Sh. G. (2014) Transformation of number presentation in modular arithmetic in RNS with different bases. Vestn. Astrakh. State Technical University. Series: Management and IT, 4: 32 - 39.
 Samoilenko, D. V., Evdokimov, A. A., Koldaev, A.I., et al. 2014. Identification of ACS subjects in RNS. Informational and communication technologies in science, industry and education (Infokom - 6): Proceedings of 6th International R&D conference, Stavropol, April 21 – 27, 2014. Part 2. – Stavropol, pp. 395 – 398.
 Knyaz`kov, V. S. and Isupov, K. S. 2015. Device for determining the signs of numbers in RNS. RF Patent, No. 2557446.
 Lyubomudrov, A. A. 2011. Device for conversion of binary code into RNS code. RF Patent, No. 2413279.
 Lyubomudrov, A. A. and Zaitsev, A. V. 2014. Method of number conversion from positional number system into residual number system. Vestn. MEPhI, 3 (2): 252 – 253.
 Lyubomudrov, A. A. and Bashkov, A. A. 2016. On Some Problems and Approach to Solution Thereof upon Computing in Residue Number System. Journal of Theoretical and Applied Informational Technology, 86: 377 - 381.
 Chervyakov, N. I., Babenko, M. G., Lyakhov, P.A., et al. 2014. Device for comparison of number represented in RNS. RF Patent, No. 2503992.
 Isupov, K. S. 2014. On an algorithm of number comparison in RNS. Vestn. Astrakh. State Technical University. Series: Management and IT, 3: 40 – 49.
 Knyaz`kov, V. S. and Osinin, I. P. 2013. Method of multiplication arrangement of floating point numbers presented in RNS. RF Patent, No. 2485574.
 Pchel`nik, V. K. and Revchuk, I. N. 2012. Implementation of Gauss method in MS Excel spreadsheets. Proceedings of International R&D conference: Informational support of engineering equipment, Moscow, April 10-11, 2012. Moscow, pp. 228 – 229.
The submitter hereby warrants that the Work (collectively, the “Materials”) is original and that he/she is the author of the Materials. To the extent the Materials incorporate text passages, figures, data or other material from the works of others, the undersigned has obtained any necessary permissions. Where necessary, the undersigned has obtained all third party permissions and consents to grant the license above and has all copies of such permissions and consents.
The submitter represents that he/she has the power and authority to make and execute this assignment. The submitter agrees to indemnify and hold harmless the COMPUSOFT from any damage or expense that may arise in the event of a breach of any of the warranties set forth above. For authenticity, validity and originality of the research paper the author/authors will be totally responsible.