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Many pattern recognition tasks employ artificial neural networks based on radial basis functions. The statistical characteristics of pattern generating processes are determined by neural networks. The Gaussian potential function is the most common radial basis function considered which includes square and exponential function calculations. The Coordinate Rotations Digital Computer, CORDIC algorithm which is used to compute the exponential function and the exponent was first derived by Volder in 1959 for calculating trigonometric functions and conversions between rectangular and polar co-ordinates. It was later developed by Walther, the CORDIC is a class of shift-add algorithms for rotating vectors in a plane. In a nutshell, the CORDIC rotator performs a rotation using a series of specific incremental rotation angles selected so that each is performed by a shift and add operation. This thesis focuses on implementation of new parallel hardware architecture to compute the Gaussian Potential Function in neural basis classifiers for pattern recognition. The new hardware proposed computes the exponential function and the exponent simultaneously in parallel thus reducing computational delay in the output function. The new CORDIC is synthesized by Altera's MAX PLUS II software for FLEX 10 K device and improvised for calculation of Radix 4. Case studies are presented and compared on the performance of Radix 2 and Radix 4 design based on the speed and the size occupied respectively. It is observed that though the area occupied by Radix 4 is more as compared to Radix 2 there is speed improvement which is desirable.