A new comparison algorithm for general 4-moduli set RNS

Residue Number System (RNS) has many applications in computer arithmetic because of its properties such as parallelism and modularity. Comparison is one of difficult operations in RNS and improving its algorithms has an important role in the use of this system for general purpose applications. In this paper a new algorithm for comparing two residue numbers in a general 4-moduli set is proposed. First, the CRT-II reverse conversion algorithm is improved using modulo decomposition and a weighted representation is obtained. Based on this approach, there is a unique weighted set to represent each number. With these weighted sets comparison is carried out similar to other weighted number systems. Comparing with previous algorithms the proposed design needs smaller modulo operations that reduce the delay. This algorithm neither assumes special conditions on the moduli set nor needs redundant modulus.