Asian Journal of Information Technology

Year: 2016
Volume: 15
Issue: 18
Page No. 3598 - 3604

Implementation of Hybrid Vedic Multiplier Nikhilam Sutra and Karatsuba Algorithm for N-bit Multiplier Using Successive Approximation of N-1 Bit Multiplier

Authors : M. Nisha Angeline and S. Valarmathy

Abstract: Vedic mathematics is the technique to solve complex arithmetic computations. Using this technique, complex problems can be solved easily. Normally, Urdhva Tiryakbhyam Sutra is generally known as Vedic Multiplier. Nikhilam Sutra is a special case in Vedic Mathematics. But there is no proper implementation hardware for Nikhilam Sutra for binary multiplication. The aim of this study is to design hardware for Nikhilam Sutra using Karatsuba algorithm using successive approximation of N-1 bit multiplier. Multipliers are the basic components used in many digital systems, digital signal processing operations and multimedia applications. Digital multipliers are the major source of power dissipation. Multiplications are often implemented with shift-and-add operations. In this study, we propose a method that combines the principles of Nikhilam sutra and Karatsuba sutra for the multiplication of binary numbers. The calculation of remainder is based on Nikhilam sutra using complement method and the weight reduction is carried out in the remainder by removing the MSB. The numerical transformation of the numbers is done by Karatsuba algorithm. For the remainder multiplication, only N-1 bit multiplier is required. Therefore, the algorithm requires only (N-1) x (N-1) bit multiplier for the calculation remainder. By combining both algorithms, the number of multiplier is reduced and also the number of bit for multiplier is also reduced. By applying this modification in the algorithm, strength of the multiplier is reduced. The research is implemented in Xilinx vertex device. The power, area and delay are measured using Cadence tool with 180 and 90nm technology. From the results’, the product of delay and area is reduced.

How to cite this article:

M. Nisha Angeline and S. Valarmathy, 2016. Implementation of Hybrid Vedic Multiplier Nikhilam Sutra and Karatsuba Algorithm for N-bit Multiplier Using Successive Approximation of N-1 Bit Multiplier. Asian Journal of Information Technology, 15: 3598-3604.

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