Determination of Multiplication Algorithm with Basis on Pascal Triangle

Abstract

Multiplication algorithms have a crucial role with occuring of approximately 10% in operating systems such as Windows, Linux, Mac OS, İOS, DOS and etc. Furthermore, these types of algorithms which are related with multiplication have to make an efficient impact on speed of CPU. Nevertheless, a lot of investigators have been making research on both improvement and optimising of methods to make a huge stride on increasing efficiency of processor’s speed. In this article, a new multiplication algorithm going to be introduced with basis on the cooperation of pascal triangle and also given specific examples about the other basic multiplication algorithms which are, Karatsuba and Nikhilam. However, results of pascal multiplication algorithm with respect to a factor of complexity analysis have been evaluated and compared to complexity of Karatsuba and classical multiplication.

Keywords

• Pascal triangle,multiplication algorithm,karatsuba

References

1. [1] D. Harvey, J. Hoeven J, G. Lecerf, Even Faster Integer Multiplication, University of New South Wales Australia, CNRS Laboratoire d’informatique Ecole Polytechnique France, (2014), 1- 28.
2. [2] S.P. Dwivedi, An efficient multiplication algorithm using Nikhilam Method, Fifth International Conference on Advances In Recent Technologies in Communication and Computing (ARTCom), (2013), 223-228.
3. [3] A. Gohill, Simultaneous multiplication of multiple numbers, Nirma University Journal of Engineering and Technology, 4(1), (2015), 6-10.
4. [4] W. B. Kandasamy, F. Smarandache, Vedic Mathematics A Fuzzy and Neutrosophic Analysis Book, (2006).
5. [5] A. Yurkin, New Analogues of Pascal Triangle and Electronic Clouds in Atoms, Russian Academy of Sciences, (2018), 1-8.
6. [6] E. Şeker. Karatsuba Algorithm, (2010), URL: http://bilgisayarkavramlari.sadievrenseker.com
7. [7] D. Matthias, Algorithmic Generator for Cambinatoric Pascal Triangle, International Journal of Physical Sciences, 2(3), (2010), 132-136.
8. [8] C. Eyüpoğlu, Performance Analysis of Karatsuba Algorithm for Different Bit Lengths, Procedia – Social and Behavioral Sciences, 195, (2015), 1860-1865.

9. [9] C. Eyüpoğlu, Investigation of Performance of Nikhilam Multiplication Algorithm, Procedia – Social and Behavioral Sciences, 195, (2015), 1959-1965.
10. [10] C. A. Tarushka, Chosen Multiplication Algorithms And The Ability To Learn New Methods, Senior Thesis Department of Mathematics and Statistics University of New Hampshire, (2013), 1-46.