An Efficient Multiplication Algorithm Using Nikhilam Method

TL;DR

This paper introduces a novel integer multiplication algorithm based on the Nikhilam method from Vedic mathematics, aiming to improve efficiency in binary multiplication within computer arithmetic.

Contribution

It presents a new multiplication algorithm leveraging the Nikhilam method, offering potential efficiency improvements over traditional binary multiplication techniques.

Findings

Potentially faster multiplication in binary arithmetic

Applicability to various integer operations

Foundation for further optimization

Abstract

Multiplication is one of the most important operation in computer arithmetic. Many integer operations such as squaring, division and computing reciprocal require same order of time as multiplication whereas some other operations such as computing GCD and residue operation require at most a factor of $\log n$ time more than multiplication. We propose an integer multiplication algorithm using Nikhilam method of Vedic mathematics which can be used to multiply two binary numbers efficiently.