Abstract
Vedic mathematics is the system of mathematics followed in ancient Indian and it is applied in various mathematical branches. The word “Vedic” represents the storehouse of all knowledge. Because using Vedic Mathematics, the arithmetical problems are solved easily. The mathematical algorithms are formed from 16 sutras and 13 up-sutras. But there are some limitations in each sutra. Here, two sutras Nikhilam sutra and Karatsuba algorithm are considered. In this research paper, a novel algorithm for binary multiplication based on Vedic mathematics is designed using bit reduction technique. Though Nikhilam sutra is used for multiplication, it is not used in all applications. Because it is special in multiplication. The remainder is derived from this sutra by reducing the remainder bit size to N-2 bit. Here, the number of bits of the remainder is constantly maintained as N-2 bits. By using Karatsuba algorithm, the overall structure of the multiplier is designed. Unlike the conventional Karatsuba algorithm, the proposed algorithm requires only one multiplier with N-2 bits only. The speed of the proposed algorithm is improved with balancing the area and the power. Even though there is a deviation in lower order bits, this method shows larger difference in higher bit lengths.
Highlights
Vedic Mathematics is the technique used in an Ancient India for solving arithmetical problems mentally and in easier way
Though Nikhilam sutra covers all range of inputs, it is efficient when the multiplicands are closer to the multiple of 10
Successive approximation of Vedic multiplier is proposed for high speed applications
Summary
Vedic Mathematics is the technique used in an Ancient India for solving arithmetical problems mentally and in easier way. It contains 16 formulas and 13 sub-formulas. These sutras are used in solving complex computations, and executing them manually. It is operated on 16 sutras and 13 up-sutras. The algorithms and principles of all sutras were given in [1]. The multiplier based on this sutra is known as Vedic multiplier. It is based on a novel concept of array multiplication. In [2], the design and implementation of Triyakbhyam were done and the speed was compared with Nikhilam sutra, squaring and cubing algorithm
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