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Smith-Waterman Algorithms (SWA) is becoming popular among researchers especially in the field of bioinformatics. The algorithm performance is better among other known alignment algorithms because of the high level of accuracy it exhibits. However, the algorithm performance is at low speed due to its computational complexity. Researchers are concerned with this problem and are looking for various ways to address the issue. Different approaches are adopted to improve the speed, such as the use of a systolic array to accelerate the algorithm, use of recursive variable expansion (RVE) method approach; some implemented the algorithm on software and hardware, etc. This paper used Residue Number System (RNS) approach to the algorithm of Smith-Waterman and carried out hardware implementation on Quartus II, 64-Bit version 12.1 (Cyclone II family) VHDL application software.