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

Abstract

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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -1, 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n+1</sup> -1}. These are needed for comparison of two numbers in residue form, base extension to modulus 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n+e</sup> 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.