Design of an RNS reverse converter for a new five-moduli special set

In this paper, we present a new residue number system (RNS) {2ⁿ-1, 2n, 2ⁿ+1, 2ⁿ⁺¹+1, 2^n-1+1} of five well-balanced moduli that are co-prime for odd n. This new RNS complements the 5-moduli RNS system proposed before for even n {2ⁿ-1, 2ⁿ, 2ⁿ+1, 2ⁿ⁺¹-1, 2^n-1-1}. With the new set, we also present a novel approach to designing multi-moduli reverse converters that focuses strongly on critical path analysis and aims at strongly on moving a significant amount of computations off the critical path. The synthesis of the resulting design over the ST Microelectronics 65nm LP library demonstrates that the delay, area, and power characteristics improve the performance and power consumption of the existing complementary 5-moduli set.