Vedic Maths in Computer Organisation

CHAPTER 1: INTRODUCTION

In ancient times, Rishis, or the saints had acquired a deep understanding of the subject and regarded Mathematics as fun and not an unavoidable drudgery. They put down their thoughts in form of Sutras, which form a part of the Atharvaveda as appendices.

The formulae as stated in Atharvaveda make calculations simple and fast by utilizing techniques like addition and subtraction accompanied with low level multiplication and division to solve complex problems of mathematics involving higher order multiplication, division, squares, cubes, square roots, cube roots etc.

Vedic mathematics is the name given to the ancient system of mathematics, or, to be precise, a unique technique of calculations based on simple rules and principles with which any mathematical problem can be solved - be it arithmetic, algebra, geometry or trigonometry. The system is based on 16 Vedic sutras or aphorisms, which are actually word formulae describing natural ways of solving a whole range of mathematical problems. Vedic mathematics was rediscovered from the ancient Indian scriptures between 1911 and 1918 by Sri Bharati Krishna Tirthaji (1884-1960), a scholar of Sanskrit, mathematics, history and philosophy [1]. He studied these ancient texts for years and, after careful investigation, was able to reconstruct a series of mathematical formulae called sutras.

Bharati Krishna Tirthaji, who was also the former Shankaracharya (major religious leader) of Puri, India, delved into the ancient Vedic texts and established the techniques of this system in his pioneering work, Vedic Mathematics (1965), which is considered the starting point for all work on Vedic mathematics. Vedic mathematics was immediately hailed as a new alternative system of mathematics when a copy of the book reached London in the late 1960s.

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Some British mathematicians, including Kenneth Williams, Andrew Nicholas and Jeremy Pickles, took interest in this new system. They extended the introductory material of Bharati Krishna's book, and delivered lectures on it in London. In 1981, this was collated into a book entitled Introductory Lectures on Vedic Mathematics [2]. A few successive trips to India by Andrew Nicholas between 1981 and 1987 renewed interest in Vedic mathematics, and scholars and teachers in India started taking it seriously.

According to Mahesh Yogi, The sutras of Vedic Mathematics are the software for the cosmic computer that runs this universe. A great deal of research is also being carried out on how to develop more powerful and easy applications of the Vedic sutras in geometry, calculus and computing.

Conventional mathematics is an integral part of engineering education since most engineering system designs are based on various mathematical approaches. All the leading manufacturers of microprocessors have developed their architectures to be suitable for conventional binary arithmetic methods. The need for faster processing speed is continuously driving major improvements in processor technologies, as well as

the search for new algorithms. The Vedic mathematics approach is totally different and considered very close to the way a human mind works. A large amount of work has so far been done in understanding various methodologies (sutras). However, hardly any meaningful applications of Vedic algorithms have been thought of. In this report, we show how a successful attempt has been made to present two and three-digit multiplication operations and the implementation of these using both conventional, as well as Vedic, mathematical methods in 8085/8086 microprocessor assembling language. We also highlight a comparative study of both approaches in terms of processing times (T states).

As we know that the computer algorithms work similar to the way we solve a problem, hence it is quite likely that a technique which requires lesser amount of effort while ____________________________________________________________

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being solved by us, if implemented in a similar fashion in a computer would have better efficiency. For instance a calculation that utilizes only addition can be performed faster than a calculation that requires multiplication or division. Hence implementing algorithms which efficiently reduce the calculations would definitely reduce the time required by the computer to find the solution to a particular problem.

In the current report we would discuss the essential calculations of multiplication, division and the calculation of square and square roots. We will find out how the effective usage of vedic sutras not only eliminates the complexity of the problem but also makes them easy to calculate within a shorter span of time.

We are looking forward to the vedic techniques towards helping us in achieving the future targets of superfast computers in super small sizes. Even with the introduction of advanced computation techniques and faster processors there is a marked requirement of faster algorithms which can help us achieve the target of faster computation techniques.

There has been substantial amount of work done towards implementing Vedic techniques in various areas which have been highlighted in chapter 2 of the current report. Chapter 3 introduces one of the basic Sutras the Nikhilam Sutram, which is widely used to carry out multiplications in a much faster way. Another technique which has been very widely used to carry out the multiplication in various research topics has been the Urdhva Tiryakbhyam Sutram, which has been completely explained and illustrated in chapter 4 of the report. Chapter 5 introduces us to one of the vedic division techniques which is efficient for carrying out division. The basic aim of the report is to concentrate on the future implementation of these vedic algorithms at the level of basic registers to carry out various arithmetic operations in a more efficient manner has been intoduced and explained in chapter 6. The next chapter stresses on the way we implement the vedic algorithms in a computer environment and brings about a few illustrations about the future implemenatation of the same.

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In chapter 8, we have a look at the various results that have been obtained for the previous observations made about the same topic. The next chapter discusses the future implementations