A reverse converter for the 4-moduli superset {2/sup n/-1, 2/sup n/, 2/sup n/+1, 2/sup n+1/+1}

Design of Reverse Converters for a New Flexible RNS Five-Moduli Set $$\{ 2^k, 2^n-1, 2^n+1, 2^{n+1}-1, 2^{n-1}-1 \}$$ { 2 k , 2 n - 1 , 2 n + 1 , 2 n + 1 - 1 , 2 n - 1 - 1 } (n Even)

“…The best-known three-moduli sets are: {2 n − 1, 2 n , 2 n + 1} -for which reverse converters have been proposed, for example in [10,22,32] -and its generalisation {2 n − 1, 2 k , 2 n + 1} with flexible even modulus 2 k , for which the reverse converter for n ≤ k ≤ 2n was proposed in [7]. The four-moduli sets include those with a single parameter n: {2 n − 1, 2 n , 2 n−1 − 1, 2 n−1 + 1} (n odd) [28], {2 n − 1, 2 n , 2 n + 1, 2 n+1 − 1} (n even) [2,3,5,28,30], {2 n , 2 n − 1, 2 n + 1, 2 n−1 − 1} (n even) [5], {2 n −1, 2 n , 2 n +1, 2 n+1 +1} (n odd) [2,29], and {2 n +1, 2 n −1, 2 n , 2 n−1 +1} (n odd) [20], as well as some of their recently proposed generalisations with a flexible even modulus 2 k : {2 k , 2 n − 1, 2 n + 1, 2 n+1 − 1} (n even and arbitrary k such that n ≤ k ≤ 2n) [6], {2 n−1 − 1, 2 n+1 − 1, 2 k , 2 n − 1} (n even and k > 2) [33] and {2 k , 2 n −1, 2 n +1, 2 n+1 −1, 2 n±1 −1} [19] (n even and k > 2). Further reduction of the widths of residue channels for a given dynamic range allow for two special five-moduli sets composed only of low-cost moduli: {2 n −1, 2 n , 2 n +1, 2 n+1 −1, 2 n−1 −1} (n even) [4] and {2 n − 1, 2 n , 2 n + 1, 2 n+1 + 1, 2 n−1 + 1} (n odd) [18].…”

A New Efficient Residue to Binary Converter for (5n+2)-bit Dynamic Range Moduli Set

“…These inherent properties make RNS very suitable to achieve a fast digital signal processing (DSP) systems including intensive computations like digital filtering, convolutions, correlations, Discrete Fourier Transform (DFT) computations, Fast Fourier Transform (FFT) computations and Direct Digital Frequency (DDF) synthesis [2]. However, RNS has not found a widespread usage in general purpose computing due to some difficult operations including overflow detection, magnitude comparison, sign detection, moduli selection, and conversion from decimal/binary to RNS and most especially the vice visa, [3], [4], [5]. Of many of these numerous RNS difficult operations, Data conversion is very critical.…”

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}

“…The DR provided by these moduli sets is not sufficient for applications which require larger dynamic range. Hence, 4n-bit DR four-moduli sets such as {2 n −1, 2 n , 2 n +1, 2 n+1 +1} [19], [20], {2 n −1, 2 n , 2 n +1, 2 n+1 − 1} [20]- [22] and {2 n − 3, 2 n + 1, 2 n − 1, 2 n + 3} [23] have been introduced. These four-moduli sets include balanced moduli, but some of their multiplicative inverses have inelegant forms which resulted in increasing the cost and the delay of the residue to binary converter.…”