Design and Implementation of Radix 4 Based Arithmetic Operations

Speed of the arithmetic operations often depends upon formation and propagation of carry. With the binary number system, the speed of arithmetic operations such as addition and subtraction is limited by formation and propagation of carry especially as the number of bits increases. The recent rapid increase in scale of integration is resulting in implementation of many sophisticated signal processing as well as video processing systems on VLSI chip in which multiplication is dominant operation. The performance of these systems is based on computation capacity and power consumption. This paper presents novel approach of multiplication scheme based on Radix 4 and implementation of addition/subtraction by using high radix system such as quaternary signed digit number system (radix-4). Using a high radix system such as quaternary signed digit number, carry free arithmetic operations can be performed. The special set of prime modulo based logic for arithmetic operations is being used in such number system. In this paper, this high radix number system is used for faster implementation of addition and subtraction. This system has been designed and simulated using Xilinx 13.4 for 8x8 bit numbers.