Reverse Conversion for Residue Number System Realizations of Digital Signal Processing Hardware

One of the fundamental problems with residue arithmetic is the difficulty associated with residue-to-binary conversion. In recently published papers, a hardware implementation of the Mixed-Radix system was proposed for the translation of residue coded outputs into binary number for a digital filter realization. These methods are presented as a block diagram or data flow chart and require integrated circuits which are not commercially available and were to be constructed from a number of basic logic elements. This paper presents a more successful technique based on a mixed-radix conversion process. The residue to binary convertor can be built using commercially available elements. To validate these results, the converters are implemented in a Standard Logic Cell of FPGA technology.