New efficient residue-to-binary converters for 4-moduli set {2n - 1, 2n, 2n + 1, 2n+1 - 1}

This paper describes a new algorithm of residue-to-binary conversion for the 4-moduli set {2ⁿ - 1, 2ⁿ, 2ⁿ + 1, 2ⁿ⁺¹ - 1} RNS which is valid for even n. The number theoretic properties of this moduli set are exploited to realize an efficient reverse converter. By using the most efficient residue-to-binary conversion algorithm for the triple moduli set {2ⁿ - 1, 2ⁿ, 2ⁿ + 1}, the problem can be reduced to a simpler residue-to-binary converter for two moduli set RNS amenable to fast mixed-radix conversion. Two different versions of architecture based on this new formulation are proposed. Comparing to the fastest reverse converter reported for the same moduli set, our proposed converters surpass it in both the area and time complexities.