Design of a novel flexible 4-moduli RNS and reverse converter

In this paper we propose a new 4-moduli Residue Number System (RNS) {2^k, 2ⁿ-1, 2^n-1 - 1, 2ⁿ⁺¹ - 1} and its respective reverse converter. The new moduli set is characterized by a very efficient way of utilizing the underlying representation´s capacity coming from its two aspects. First, by not including conjugate moduli our set covers the dynamic range of the representation much better than the systems that do include conjugate moduli. Second, independent controlling parameters of the even and odd moduli allow for fine-grained adjustment of the dynamic range to the needs of specific application with a single bit resolution. Our converter capitalizes on the mixed-radix conversion technique augmented to obtain a compact architecture and to reduce critical path delay by careful decomposition of the computations into cricital and non-critical chunks. The synthesis experiment conducted on a 16-tap programmable FIR filter example using STMicro 65nm low-power library shows up to 11.5% improvement in power dissipation against competitive flexible moduli set.