An efficient algorithm and implementation for residue to binary number conversion

The residue number system (RNS) has computational advantages in addition and multiplication compared with weighted number systems, such as the binary number system (BNS), since operations on residue digits are performed independently and these processes can be performed in parallel. Thus they are widely used in digital signal processing etc. Since residue to binary conversion is critical and difficult for the practicality of RNS, in this paper, a novel residue to binary (R/B) conversion algorithm for the restricted moduli set (2ⁿ -1, 2ⁿ, 2n+1), based on exploring the periodicity of modulo (2ⁿ ± 1) operations is presented. A new 2n-bit adder based R/B converter is also proposed. The performance comparison results demonstrate that the new converter is faster and requires less area compared with the others reported in the previous literature.