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With rapid increase in scale of integration, many sophisticated signal processing as well as video processing operations are being implemented on VLSI chips. Various arithmetic modules are used in such systems. The performance in very-large-scale-integrated (VLSI) systems such as digital signal processing (DSP) chips is predominantly determined by the speed of arithmetic modules like adders and multipliers.This thesis deals with design and implementation of three basic arithmetic operations viz., multiplication, addition and subtraction based on Radix-4 algorithm. These arithmetic operations based on Radix-4 algorithm reduces number of iterations and helps to speed up operation. With increase in the speed of system, overall performance of system increases too.