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
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Author
Jeffrey Uhlmann, Department of Electrical Engineering and Computer Science, University of Missouri, Columbia, USA
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Abstract
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.
Keywords
Binary Numbers, Number Systems, Mathematics Education, Number Theory, Prime Factorization, Prime Numbers
To cite this article
Jeffrey Uhlmann, A Product-Based Binary Number System, Applied and Computational Mathematics. Vol. 7, No. 5, 2018, pp. 217-218. doi: 10.11648/j.acm.20180705.11
Copyright
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.
References
[1]
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.
[2]
Herstein, I. N., Abstract Algebra, Macmillan Publishing, p. 30, 1986.
[3]
Donald Knuth, The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, 3rd Edition, Addison-Wesley, 1997.
[4]
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.
[5]
Uhlmann, J. K., (1995). Dynamic Map Building and Localization: New Theoretical Foundations, A16, pp. 243-24, Doctoral Dissertation, University of Oxford.
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