Implementation of Arithmetic Operations in the Residue Numeral System

To improve the performance of computer systems, special number systems can be used, for example, the residue numeral system (RNS). Replacing integers with their values modulo several pairwise coprime integers (called the moduli) can significantly reduce the complexity of arithmetic operations. However, the different way of representing numbers makes it difficult to use RNS in practice. For example, integers represented in a positional numeral system need to be quickly converted to RNS and vice versa. In addition, the implementation of computing devices operating in the RNS must also take into account the peculiarities of representing numbers as residuals on coprime bases. In this article, we look at the various structures of computing devices in RNS. In particular, we present the arithmetic operations of addition modulo and give examples of adders.