Evaluation of Mixed-Radix Digit Computation Techniques for the Three Moduli RNS {2n-1, 2n, 2n+1-1}

In this brief, we evaluate two techniques for obtaining mixed-radix digits using mixed-radix conversion technique, for the residue number system (RNS) moduli set {2(n) - 1, 2(n), 2(n+1) - 1}. These are needed for comparison of two numbers in residue form, base extension to modulus 2(n+e) and reverse conversion. The complete architectures are derived to estimate the hardware resource requirement and computation time for deriving the mixed-radix digits. The proposed techniques are also compared with designs based on other techniques available in literature. The trade-offs regarding hardware resource requirement, computation time and power dissipation are brought out.