In this paper, an implementation method for digital filters using the residue arithmetic is proposed. This method can be used for processing digital signals with larger number of bits by applying the idea of the bit-slice algorithm, while previous residue digital filters can process digital signals with only a small number of bits. Furthermore, high-speed residue addition, subtrac-tion, and multiplication using look-up tables make it possible to get more flexible filters. Everything that is mentioned above is proved by implementing a cascade fourth-order Butterworth lowpass digital filter using this method.