Residue number systems have gained significant importance in the field of high-speed digital signal processing due to their carry-free nature and speed-up provided by parallelism. The critical aspect in the application of RNS is the selection of the moduli set and the design of the conversion units. There have been several RNS moduli sets proposed for the implementation of digital filters. However, some are unbalanced and some do not provide the required dynamic range. This thesis addresses the drawbacks of existing RNS moduli sets and proposes a new moduli set for efficient implementation of FIR filters. An efficient VLSI implementation model has been derived for the design of a reverse converter from RNS to the conventional two's complement representation. This model facilitates the realization of a reverse converter for better performance with less hardware complexity when compared with the reverse converter designs of the existing balanced 4-moduli sets. Experimental results comparing multiply and accumulate units using RNS that are implemented using the proposed four-moduli set with the state-of-the-art balanced four-moduli sets, show large improvements in area (46%) and power (43%) reduction for various dynamic ranges. RNS FIR filters using the proposed moduli-set and existing balanced 4-moduli set are implemented in RTL and compared for chip area and power and observed 20% improvements. This thesis also presents threshold logic implementation of the reverse converter.