31-08-2017, 03:41 PM
In this article we propose a reduced bit multiplication algorithm based on the old Vedic multiplication formulas. Both the Vedic multiplication formulas, Urdhva tiryakbhyam and Nikhilam, are discussed first in detail. Urdhva tiryakbhyam, which is a general formula of multiplication, is equally applicable to all cases of multiplication. It is applied to digital arithmetic and is shown to produce a multiplier architecture that is very similar to the popular array multiplier. Due to its structure, it leads to a propagation delay of high retention in case of multiplication of large numbers. Nikhilam Sutra, on the other hand, is more efficient in multiplying large numbers, since it reduces the multiplication of two large numbers to that of two smaller numbers. The framework of the proposed algorithm is taken from this Sutra and further optimized by the use of some general arithmetic operations such as expansion and shifting of bits to take advantage of bit reduction in multiplication.