Efficient MRC-Based Residue to Binary Converters for the New Moduli Sets {22n, 2n-1, 2n+1-1} and {22n, 2n-1, 2n-1-1}

In this paper, the new residue number system (RNS) moduli sets {2(2n), 2(n) - 1, 2(n+1) - 1} and {2(2n), 2(n) - 1, 2(n-1) - 1} are introduced. These moduli sets have 4n-bit dynamic range and well-formed moduli which can result in high-performance residue to binary converters as well as efficient RNS arithmetic unit. Next, efficient residue to binary converters for the proposed moduli sets based on mixed-radix conversion (MRC) algorithm are presented. The converters are ROM-free and they are realized using carry-save adders and modulo adders. Comparison with the other residue to binary converters for 4n-bit dynamic range moduli sets shown that the presented designs based on new moduli sets {2(2n), 2(n) - 1, 2(n+1) - 1} and {2(2n), 2(n) - 1, 2(n-1) - 1} are improved the conversion delay and result in hardware savings. Also, the proposed moduli sets can lead to efficient binary to residue converters, and they can speed-up internal RNS arithmetic processing, compared with the other 4n-bit dynamic range moduli sets.