An approach to comparing number modules in number systems in residual

Abstract

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 n and n, respectively, where n = restА mod pn and n = restB mod pn. Next, access to the computer memory at the addresses (1, 2, . . ., n-1) and (1, 2, . . . ., n-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 n and n. 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.