An Introduction to Vedic Mathematics

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 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

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

Author - Hemika Yadav

(Intern at Silicon Mentor)

Importance of M.Tech/M.E Paper Publication

The industry oriented programs in engineering and information technology are increasing day by day. There are many educational degree program in engineering offered by IIT’s/BITS/NIT’s and other educational institutions. The M.Tech (Master of Technology)/M.E in VLSI is one of the prestigious engineering degree program. The Course curriculum for M.Tech/M.E in VLSI is divided as follows: 

Sem-1 Regular subjects + 1 Minor project

Sem-2 Regular subjects + 1 Major project

Sem-3 Regular subjects + Dissertation/Thesis part -1

Sem-4 Dissertation/Thesis part-2 

As, the course curriculum mainly depends on projects and thesis, it needs IEEE based VLSI Projects [According to the impact factor and recent research publication on critical and innovative topics the IEEE known to be the best source for research supporting data].The VLSI thesis/projects are divided in two parts, VLSI front-end projects and VLSI back-end projects. The main motto to describe about M.Tech [VLSI] is to tell you about the importance of paper publication during masters. The importance can be understood with a story:

“Let us suppose you are doing a project/ thesis and you have to show your project description to some of the organization/company that is far away from your home location, in that condition you have two option either you send your whole docs soft copy or send him short summery [1 page] of your work with your online published paper’s link. In the first option most probably the organization would not believe on your project work because each have not much time to read a 100 pages description but if you choose second option then you have to publish you work on line and once your research work shall be on line then anybody may see or access you research paper. Sometimes some big researchers call some bright researchers to work with him by their on line published papers. ”

Therefore the conclusion of the story is the M.Tech paper publication is must and necessary to grab new opportunities in the world of growing technologies. 
                                                                    
                                                       
                                                              Author- Dinesh Chauhan 

      (Research Associate at Silicon Mentor)