Simple binary to residue transformation with respect to 2m +1 moduli

The residue number system (RNS) is suitable for implementing most digital signal processing (DSP) algorithms where addition, subtraction and multiplication are predominant. These operations are performed without carry propagation. However, before any processing can be started, the input binary number must be converted into the residue number format. This conversion is an overhead to the performance of the system. Most implementations of binary to residue convertors are based on ROMs, which are slow and costly. The authors derive a new formula for transforming conventional binary numbers into residue representation with respect to the 2^m+1 moduli. Using the derived format, we can partition the input binary number into consecutive m-bit sections. This increases the speed and reduces the hardware complexity compared with the existing memory based methods. We also present an m-bit partitioned architecture for converting binary numbers into residue format with respect to the {2^m-1, 2^m, 2^m+1} moduli set