Perspective and Opportunities of Modulo 2n-1 Multipliers in Residue Number System: A Review

Modulo multiplier has been attracting considerable attention as one of the essential components of residue number system (RNS)-based computational circuits. This paper contributes a comprehensive review in the design of modulo 2(n) - 1 multipliers for the first time. The modulo multipliers can be implemented using ROM (look-up-table) as well as VLSI components (memoryless); however, the former is preferable for lower word-length and later for larger wordlength. The modular and parallelism properties of RNS are used to improve the performance of memoryless multipliers. Moreover, a Booth-encoding algorithm is used to speed-up the multipliers. Also, an advanced modulo 2(n) - 1 multiplier based on redundant RNS (RRNS) could be further chosen for very high dynamic range. These perspectives of modulo 2(n) - 1 multipliers have been extensively studied for recent state-of-the-art and analyzed using Synopsis design compiler tool.