A Product-Based Binary Number System
Applied and Computational Mathematics
Volume 7, Issue 5, October 2018, Pages: 217-218
Received: Dec. 10, 2018;
Accepted: Jan. 2, 2019;
Published: Jan. 28, 2019
Views 411 Downloads 81
Jeffrey Uhlmann, Department of Electrical Engineering and Computer Science, University of Missouri, Columbia, USA
Follow on us
The fundamental theorem of arithmetic says that every natural number greater than 1 is either a prime itself or can be factorized as a product of a unique multiset of primes. Every such integer can also be uniquely decomposed as a sum of powers of 2. In this note we point out that these facts can be combined to develop a binary number system which uniquely represents each integer as the product of a subset of a special set of prime powers which we refer to as P-primes.
Binary Numbers, Number Systems, Mathematics Education, Number Theory, Prime Factorization, Prime Numbers
To cite this article
A Product-Based Binary Number System, Applied and Computational Mathematics.
Vol. 7, No. 5,
2018, pp. 217-218.
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
E. C. R. Hehner and R. N. S. Horspool, “A new representation of the rational numbers for fast easy arithmetic,” SIAM Journal of Computing. 8:2, pp. 124-134, 1979.
Herstein, I. N., Abstract Algebra, Macmillan Publishing, p. 30, 1986.
Donald Knuth, The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 3rd Edition, Addison-Wesley, 1997.
C. Serpa and J. Buesca, “Piecewise Expanding Maps: Combinatorics, Dynamics and Representation of Rational Numbers,” ESAIM: Proceedings and Surveys, Vol. 46, pp. 213-216, 2014.
Uhlmann, J. K., (1995). Dynamic Map Building and Localization: New Theoretical Foundations, A16, pp. 243-24, Doctoral Dissertation, University of Oxford.