A reverse converter for the new 4-moduli set {2n + 3, 2n + 2, 2n + 1, 2n}

Abstract

In this paper, we propose a new 4-moduli set {2n + 3, 2n + 2, 2n + 1, 2n} that increases the dynamic range and the processing parallelism enabling efficient reverse conversion. First, we assume a general 4-moduli set {m i }i=1,4, m 1 ≫ m 2 ≫ m 3 ≫ m 4 , with the dynamic range M = Π4 i=1 m i and introduce a modified Chinese Remainder Theorem (CRT) that requires mod-m 4 instead of mod-M calculations. Subsequently, we further simplify the conversion process by focussing on the {2n + 3, 2n + 2, 2n + 1, 2n} moduli set, which has a common factor of 2. Given that for such a moduli set, CRT cannot be directly applied, we introduce a CRT based approach for this case, which first requires the conversion of {2n + 3, 2n + 2, 2n + 1, 2n} set into the moduli set with relatively prime moduli, i.e., {m 1 , m 2 /2, m 3 , m 4 }, valid for n even, which are not multiples of 3. We demonstrate that such a conversion can be easily done and doesn't require the computation of any multiplicative inverses. For this case, the proposed CRT utilizes the same or slightly larger area when compared to other existing techniques but all the operations are mod-m 4 . This outperforms state of the art CRTs in terms of the magnitude of the numbers involved in the calculation and due to this fact, our proposal results in less complex adders and multipliers.