Using the 2 n Property to Implement an Efficient General Purpose Residue-to-Binary Converter

Even though it has been shown that residue number systems (RNS) provide very fast and reliable arithmetic due to its inherent parallel processing and error correction capabilities, its use is severely limited to a few applications due to the complexities involved in its conversion circuitry. Hence the design of efficient converters is still considered an important area of research in RNS based processor designs. In this regard, we present an area efficient residue-to-binary converter based on the Chinese Remainder Theorem (CRT). It can be shown that if one of the moduli is an integer power of 2 (of the form 2), we need not calculate the lower order n bits of the number while performing the reverse conversion. For a look up table implementation this will reduce the width of the table by n bits. This brings about 15% reduction in overall hardware complexity for a 32 bit reverse converter and a speed up equivalent of n full adder delays compared to previous designs.