With the sequencing of DNA becoming cheaper and the resulting stack of data growing bigger, there is a big challenge for both engineer and biologist. Researchers are limited by their computational power. In this thesis, first an overview of sequence alignment algorithms will be given. Then a method to store the values of the similarity score matrix of the Smith-Waterman algorithm differentially will be presented. And finally, a description of the system approach used to design an accelerator, which implements this method, will be given. Implementation of the system design on an Artix-7 XC7A200T-2C FPGA, could lead to a total performance of 94 GCU/s. This is a speed up of 5x compared to conventional CPUs.