Vedic mathematics is the ancient
name of mathematics that was rediscovered in twentieth century. Vedic
Mathematics has a unique technique of calculations based on 16 Sutras.

A simple digital multiplier
(referred henceforth as Vedic multiplier) architecture based on the Urdhva
Triyakbhyam (means vertically and Cross wise) Sutra is explained. Urdhva – Triyakbhyam

*is the general formula which is applicable to all cases of multiplication.*
The beauty of Vedic multiplier is
that here partial product generation and additions are done concurrently or
simultaneously. Hence, it is well adapted to parallel processing. The feature
makes it more attractive for binary multiplications. This in turn reduces delay
and reduces complex calculations into simple one. In most of the dsp
applications, the critical operations are multiplication and accumulation.

The method is explained below for
two, 2 bit numbers A

Tags : Vedic mathematics Vedic Multiplier Vedic Methods Introduction to Vedic Mathematics

*and B**where A**= a1a0 and B = b1b0. Firstly, the least significant bits are multiplied which gives the least significant bit of the final product (vertical). Then, the LSB of the multiplicand is multiplied with the next higher bit of the multiplier and added with, the product of LSB of multiplier and next higher bit of the multiplicand (crosswise). The sum gives second bit of the final product and the carry is added with the partial product obtained by multiplying the most significant bits to give the sum and carry. The sum is the third corresponding bit and carry becomes the fourth bit of the final product. The 2X2 Vedic multiplier module is implemented by four input AND gates & two half-adders.* method for 4x4 Vedic multiplier | |

It
is found that the hardware architecture of 2x2 bit Vedic multiplier is same as
the hardware architecture of 2x2 bit conventional Array Multiplier.

Hence
it is concluded that multiplication of 2 bit binary numbers by Vedic method
does not made significant effect in improvement of the multiplier’s efficiency.
The 4x4 bit Vedic multiplier module is implemented using four 2x2 bit Vedic
multiplier modules as shown above.

In
4x4 multiplications, A= a3 a2 a1 a0 and B= b3 b2 b1 b0. The output line for the
multiplication result is – s7s6s5s4 s3s2 s1 s0 and carry is ca2ca3.The main
advantage behind this architecture is that the area needed for Vedic multiplier
is very small as compared to other multiplier architecture.

hardware architecture
of 4x4 multiplier |

Author - Hemika Yadav

(Intern at Silicon Mentor)