Abstract

The residue number system (RNS) allows high accuracy integer-valued arithmetic operations to be decomposed into independent (carry-free), low accuracy computations that can be performed in parallel. The RNS thus provides an attractive alternative to weighted number systems (e.g., binary or decimal) for high speed numerical computing¹. The residue number representation is completely specified by a set of relatively prime moduli. The overall dynamic range is given by the product fo the moduli. Although this dynamic range can be arbitrarily high, the dynamic range required in any individual subcalculation is commensurate only with the associated modulus. The RNS also leads to a reduction in the growth of the total number of combinatorial logic elements required to perform a calculation via truth table approach. Specifically, the RNS exhibits additive growth in spatial complexity with input word size, contrasted by multiplicative (exponential) growth for weighted number systems.

© 1989 Optical Society of America