Design of a high speed reverse converter for a new 4-moduli set residue number system

This paper presents an elegant residue-to-binary algorithm for a new 4-moduli set (2ⁿ - 1, 2ⁿ, 2ⁿ + 1, 2²ⁿ + 1) Residue Number System. Our reverse conversion algorithm takes advantage of the special number properties of the proposed moduli set. The recently introduced New CRT theorem has been exploited to simplify the costly and time consuming modular corrections. The resulting architecture is notably simple and can be realized in hardware with only bit reorientation operation and a Multi-Operand Modular Adder. In terms of area-time complexity, the performance of the new reverse converter surpasses previously reported reverse converters for several celebrated four-moduli sets.