Explanation of the principles of the Booth algorithm, Verilog implementation and simulation

Wangye Jiang

doi:10.54097/w2trr971

Authors

Wangye Jiang

DOI:

https://doi.org/10.54097/w2trr971

Keywords:

Computational Efficiency, Booth Algorithm, Multipliers, Algorithmic Tools.

Abstract

In an era marked by heightened constraints on computer processing speed and storage capacity, optimizing computational efficiency and space utilization assumes paramount importance. Consequently, the deployment of proficient algorithmic tools holds significant significance within the realm of computing. The principal categories of multipliers encompass conventional multipliers, shift-and-add multipliers, Look-Up Table (LUT) multipliers, and Booth algorithm multipliers. Among these, the Booth algorithm substantially influences multiplier performance enhancement. This paper investigation commences with a comprehensive elucidation of the mathematical underpinnings of the Booth algorithm. Subsequently, it involves the development of code corresponding to the mathematical expressions, which is executed within the VIVADO environment. Given the inherent simplicity of the experiment, virtual simulation is directly conducted in VIVADO. The analysis is grounded in the examination of data waveforms. Ultimately, the output waveform is correlated with the BOOTH mathematical formula, culminating in the successful implementation of the BOOTH algorithm. This paper aims to effectively curtail the presence of '1's in computer data, thereby reducing the computational steps and conserving operational space. This, in turn, leads to a notable acceleration in the computational speed, accomplishing the objective of enhancing computational efficiency.

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