An effective New CRT based reverse converter for a novel moduli set {22n+1 - 1, 22n+1, 22n - 1}

In this paper, a novel 3-moduli set { 2 − 1, 2, 2 − 1 } , which has larger dynamic range when compared to other existing 3-moduli sets is proposed. After providing a proof that this moduli set always results in legitimate RNS, we subsequently propose an associated reverse converter based on the New Chinese Remainder Theorem. The proposed reverse converter has a delay of (4n + 6)tFA with an area cost of (8n + 2)FAs and (4n − 2)HAs, where FA, HA, and tFA represent Full Adder, Half Adder, and delay of a Full Adder, respectively. We compared the proposed reverse converter with state of the art converters for similar or equal dynamic range RNS and our analysis indicate that for the same dynamic range the best converter requires (16n + 1)FAs and exhibits a delay of (8n+2)tFA. This indicates that, theoretically speaking, our proposal achieves about 37.5% area reduction and it is about 2 times faster than equivalent state of the art converters. Moreover, the product of the area with the square of the delay is improved up to about 84.4% over the state of the art. Keywords—Moduli Set, Dynamic Range, Reverse Converter, Chinese Remainder Theorem, New Chinese Remainder Theorem.