Applied and Computational Mathematics

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A Product-Based Binary Number System

Received: 10 December 2018    Accepted: 02 January 2019    Published: 28 January 2019
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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.

DOI 10.11648/j.acm.20180705.11
Published in Applied and Computational Mathematics (Volume 7, Issue 5, October 2018)
Page(s) 217-218
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Binary Numbers, Number Systems, Mathematics Education, Number Theory, Prime Factorization, Prime Numbers

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.
Author Information
  • Department of Electrical Engineering and Computer Science, University of Missouri, Columbia, USA

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    Jeffrey Uhlmann. (2019). A Product-Based Binary Number System. Applied and Computational Mathematics, 7(5), 217-218. https://doi.org/10.11648/j.acm.20180705.11

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    Jeffrey Uhlmann. A Product-Based Binary Number System. Appl. Comput. Math. 2019, 7(5), 217-218. doi: 10.11648/j.acm.20180705.11

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    Jeffrey Uhlmann. A Product-Based Binary Number System. Appl Comput Math. 2019;7(5):217-218. doi: 10.11648/j.acm.20180705.11

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      title = {A Product-Based Binary Number System},
      journal = {Applied and Computational Mathematics},
      volume = {7},
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      doi = {10.11648/j.acm.20180705.11},
      url = {https://doi.org/10.11648/j.acm.20180705.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20180705.11},
      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.},
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