New area efficient residue-to-weighted number system converters

The residue number system is popular in high performance arithmetic applications like digital signal processing because of its carry free nature, modularity and error correcting properties. But these opportunities are eclipsed by the high area and time requirements for reverse conversion. In this regard, we present two new techniques for residue-to-weighted number system conversion. The first one is based on the popular Chinese remainder theorem. Here by evaluating the quotient the number is decoded. The second one deals with residue-to-mixed radix conversions. The arithmetic based technique replaces the conventional hardware intensive look up tables by simple adders. An OHR based high speed MRC is also presented. The mixed radix converters described are memoryless and are hardware efficient compared to conventional techniques