Modulized RNS-decimal number conversion algorithm and its implementations

Abstract

An investigation is conducted into residue number system (RNS) to decimal number system conversion algorithms and their implementations. For general Q-tuple RNS decoding, the authors propose a modularized decoding algorithm in which each module decodes only a 2-tuple RNS code, and they discuss its computational complexity at the algorithm level. The second algorithm is for decoding a 2-tuple RNS code and can be called a partial table-lookup method. By memorizing only partial decimal numbers in the dynamic range of any RNS, this method can generate the correct decimal number with at most three additions. Hardware implementation methods are discussed, and a comparison of the algorithms with conventional decoding algorithms is made in terms of the arithmetic operation complexity, dynamic range requirements, and hardware implementation complexity.<>