In this paper we present an RNS algorithm and architecture implementation of gene sequence applications based on an existing RNS arithmetic algorithm. Investigation was made on RNS application and its inherent arithmetic advantages; data conversion algorithm from Decimal/Binary to RNS; the forward conversion; Conversion from RNS to Binary/Decimal; the reverse conversion using the Chinese remainder theorem CRT, conversion from RNS to mixed radix form with capability for effective computation performance, and analysis of Smith Waterman Algorithm based on DNA sequence computing. Its limitations and open issues for future research were highlighted.