Improved mixed-radix conversion for residue number system architectures

Processor architectures, based on arithmetic cells using residue number systems, are inherently parallel, modular and fault isolating. The fundamental characteristic of a residue number system is its being an unweighted numbering system. The authors describe an improved technique for transforming a residue number into a mixed-radix weighted representation. The proposed conversion algorithm is based on the cyclic patterns inherent in residue number systems. The mixed-radix digits of the proposed conversion procedure are factorised into a product of two terms each: one term is invariant and predetermined, whereas the other is variable and depends upon the particular residue number being converted. In comparison with existing conversion techniques, the proposed conversion method achieves a considerable reduction in the number of arithmetic multiplications needed during the conversion process