On residue number system decoding

The use of a residue number system (RNS) in digital systems and especially filter designs is facilitated by efficient algorithms for the conversion from RNS to binary numbers. The conversion is generally based on the Chinese remainder theorem or the mixed radix conversion. This correspondence describes another conversion algorithm which employs the direct pairwise solution of the Diophantine equations defining the number in the given moduli set. The algorithm provides a high degree of parallel computation.