Vedic mathematics:
• Vedic mathematics is primarily the 16 sutras and their applications in order to carry out the tedious and difficult arithmetic operations, and to a very large extent perform them mentally.
• Nikhilam NavatascaramamDasatahSutra (or simply Nikhilam Sutra) is one of the 16 sutras is used for multiplication, and has been used successfully to overcome the drawbacks of the conventional system. This is where modern computing and Vedic mathematics converge.
The need for efficient multiplication algorithm:
• The use of numerical methods is widespread in most software algorithms. Such applications require an efficient code for basic mathematical operations, one of them as multiplication.
• Real-time system requires immediate reaction environment variables and rapid implementation of the decisions taken.
• Multiplication algorithms find application in Digital Signal Processing (DSP) for Discrete Fourier Transforms, Fast Fourier Transforms, convolution, digital filters, etc. Why open a new multiplication algorithm up a new strategy to improve the existing system.
This requires a "time efficient" algorithm "multiplication" to improve CPU throughput.
Explanation of the Nikhilam Sutra:
One of the 16 sutras of Vedic mathematics, Nikhilam Sutra stated algebraically as follows:
Consider two numbers n1 and n2such as
N1 = (x – a); a = (x – n1)
N2 = (x-b), b = (x-n2)
Where x = a, b = base, differences from base, then
N1 x n2 = (x-a) (x-b) = x [(x – a) + (x-b) – x] + a * b
Thus the Nikhilam Sutra effectively broke a big multiplication n1 x n2 to a little multiplication (a x b) and additions [(x – a) + (x-b) – x].
Decimal multiplication with the Nikhilam Sutra:
• 99 x 98:
Base with 10, n1 and n2 is less than the Base:
Consider n1 = n2 = 99 and 98
Number of difference base x
(x - a) = 99 a = time difference
100
(x-b) = 98 (b) = + 02
(x-a) + (x-b) – x = 97 * b = 02
Product: 9702
Algorithm for Radix 2 ...
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