vedic

Slide 1:

Vedic mathematics is the name given to the ancient Indian system of mathematics that was rediscovered in early twentieth century. The word ‘Vedic’ is derived from the word ‘Veda’ which means the store-house of all knowledge. Vedic mathematics was reconstructed from the ancient Indian scriptures (Vedas) by Swami Bharati Krishna Tirthaji, (1884-1960) after his eight years of research on Vedas Vedic mathematics is mainly based on 16 Sutras (or aphorisms) dealing with various branches of mathematics like arithmetic, algebra, geometry etc. Vedic Mathematics

Slide 2:

Benefits of Vedic Mathematics Vedic Mathematics is becoming popular all over the world due to the following: It helps a person to solve problems 10-15 times faster. It reduces burden (Need to learn tables up to nine only) It provides one line answer. It is a magical tool to reduce scratch work and finger counting. It increases concentration. Time saved can be used to answer more questions

Slide 3:

Objective The main objective of this paper is to design and implementation of a fast multiplier with self testing, which can be used in any processor application. Multiplication is an important fundamental function in many Digital Signal Processing (DSP) applications such as convolution, Fast Fourier Transform(FFT), filtering and in microprocessors in its arithmetic and logic unit . Since multiplication dominates the execution time of most DSP algorithms, so there is a need of high speed multiplier. Multiplier based on Vedic Mathematics is one of the fast and low power multiplier .

Slide 4:

Vertically and crosswise Urdhva Tiryakbhyam is the Sanskrit term for “Vertically and crosswise”. This formula applies to all cases of multiplication and is very useful in division of one large number by another large number.

Urdhva – tiryagbhyam (Vertical & Crosswise Multiplication):

Urdhva – tiryagbhyam (Vertical & Crosswise Multiplication) Procedure for product of 14 and 21. Step 1: Right 4 2 1 : 4 x 1 = 4 Step 2: Middle 4 2 1 : 1 x 1 + 2 x 4= 9 Step 3: Left 1 4 2 1 :1 x 2=2 So, it gives result as 294 Left Middle Right

Proposed Hardware Architecture for Vertical & crosswise multiplication:

Proposed Hardware Architecture for Vertical & crosswise multiplication Multiplier Multiplier Multiplier Multiplier A B C D A B D C Adder Left Middle Right

Slide 7:

ADDER ADDER ADDER ADDER ADDER ADDER Hardware Architecture for 4 – Bit Multiplier

The Wave window for the vertical & Crosswise Multiplication  :

The Wave window for the vertical & Crosswise Multiplication

Slide 9:

By one more than the one before Ekadhikena Purvena" is the Sanskrit term for “by One more than the previous one". It provides a simple way of calculating values like computing squares of numbers ending in five. It can also be applied in multiplications when the last digit is not 5 but the sum of the last digits is the base (10) and the previous parts are the same.

VEDIC ALGORITHM FOR SQUARING A NUMBER ENDING WITH FIVE :

VEDIC ALGORITHM FOR SQUARING A NUMBER ENDING WITH FIVE Algorithm for square of 25 Step 1: Let xy= 25 x = 2, y = 5 = 25; Left= x(x+1); Left = 2(2+1) = 6; Right = = 25; Final Answer = 625;

Hardware Architecture of the proposed squaring a number ending with five. :

Hardware Architecture of the proposed squaring a number ending with five . A 0001 11001 Parallel Adder Multiply Left Right

The Wave window for the squaring a number ending with five.   :

The Wave window for the squaring a number ending with five.

VEDIC ALGORITHM FOR SUM OF THE LAST DIGITS IS THE BASE (10) AND PREVIOUS PARTS ARE THE SAME :

VEDIC ALGORITHM FOR SUM OF THE LAST DIGITS IS THE BASE (10) AND PREVIOUS PARTS ARE THE SAME Let us take 57 x 53 1.A = 5,B=7,A=5,C=3 2.Now the number becomes 573 3.Now Multiply B & C,7 X 3=21. 4.Now multiply A & A+1,we get 5 x6 = 30 5.Now the Result is 3021.

Hardware Architecture of the proposed algorithm for the sum of the last digits is the base(10) and previous parts are the same. :

Hardware Architecture of the proposed algorithm for the sum of the last digits is the base(10) and previous parts are the same. A B A C A B C Multiply A+1 Multiply Left Right

The Wave window for the sum of the last digits is the base(10) and previous parts are the same.   :

The Wave window for the sum of the last digits is the base(10) and previous parts are the same.