A Fully Parallel Mixed-Radix Conversion Algorithm for Residue Number Applications

Abstract

A new, fully parallel mixed-radix conversion (MRC) algorithm which utilizes the maximum parallelism that exists in the residues (RNS) to mixed-radix (MR) digits conversion to achieve high throughput rate and very short conversion time is presented. The new algorithm has a conversion time of two table look-up cycles for moduli sets consisting of up to 15 moduli. As a comparison, the classical Szabo and Tanaka MRC algorithm has a conversion time of (n − 1) clock cycles for an n-moduli RNS. This algorithm can be implemented by off-the-shelf ECL IC's to achieve a conversion time of 50 ns and a throughput rate of 40 MHz for a 150-bit RNS.