Design and Implementation of an Efficient 32-Bit Fixed-Point Newton-Raphson Division-Based Reciprocal Computing Unit

Reciprocal operations play a critical role in digital signal processing (DSP), specifically in the execution of linear equation solving and Fourier analysis. For DSP architectures to support functions like adaptive filtering, channel equalization, and spectral estimation, efficient reciprocal computation is vital. Reciprocal computations frequently employ the Newton-Raphson algorithm, which is flexible concerning both floating-point and fixed-point formats. This paper proposes a digital design architecture of the reciprocal computing unit using the Newton Raphson method, which is modeled, and implemented using Verilog HDL, and the Xilinx Vivado Tool. Enhanced accuracy and substantial reductions in error rates are successfully attained using the proposed design. The average mean error rate of roughly 0.0264 % is associated with converging values. The design uses optimized resources by decreasing the required logic elements by an average of 15.76%. The results of our study emphasize the capability of our design and methodology to improve both computational efficiency and accuracy in DSP applications.