Adder based residue to binary converters for a new balanced 4-moduli set

In this paper, an efficient residue to binary conversion algorithm is derived for a new four-moduli set {2ⁿ-1, 2ⁿ, 2ⁿ+1, 2^n-1-1} with large dynamic range and well-balanced moduli. Our algorithm exploits the special periodicity properties of the proposed moduli set to obtain hardware efficacy. By using the most efficient residue to binary conversion of the three-moduli set {2ⁿ-1, 2ⁿ, 2ⁿ+1}, the proposed algorithm can be reduced to a simpler two moduli set RNS where fast mixed-radix conversion can be used to obtain the weighted binary number. Four different adder-based architectures are proposed, all are pipelinable to achieve very high throughput rate, and all are more efficient than the residue to binary converters for other four-moduli sets in terms of area and delay.