Pure and Applied Mathematics Journal

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Numeral System Change in Arithmetic and Matricial Formalism

Received: 12 May 2016    Accepted: 25 May 2016    Published: 07 June 2016
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Abstract

The main goal of this paper is to present a method to tackle the numeral system change problem using matricial formalism. In a previous work, we have described an approach which permits to use matricial formalism and matricial calculation in writing numeration and arithmetic. The present paper is focused on the study of the problem of numeral system change in the framework of this approach. The cases of integer numbers and of more general numbers are given.

DOI 10.11648/j.pamj.20160503.15
Published in Pure and Applied Mathematics Journal (Volume 5, Issue 3, June 2016)
Page(s) 87-92
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

Numeral System, Arithmetic, Radix, Matricial Formalism, Basis Change

References
[1] Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Wilfrid Chrysante Solofoarisina. “Arithmetics and Matricial Calculation”, Science Publishing Group, Pure and Applied Mathematics Journal (on press), 2016.
[2] Raoelina Andriambololona, “Algèbre linéaire et multilinéaire”, Collection LIRA, INSTN-Madagascar, Antananarivo, Madagascar, 1986.
[3] Anton Howard, Chris Rorres, “Elementary Linear Algebra” (10th ed.), John Wiley & Sons, 2010.
[4] William C. Brown “Matrices and vector spaces”, New York, NY: Marcel Dekker, 1991.
[5] Georges Ifrah, David Bellos, E. F. Harding, Sophie Wood, Ian Monk, “The Universal History of Numbers: From Prehistory to the Invention of the Computer”, John Wiley & Sons, New York, 1999.
[6] Stephen Chrisomalis, “Numerical Notation: A Comparative History”, Cambridge University Press, 2010.
[7] Anton Glaser, “History of binary and other nondecimal numeration”, Tomash, 1971.
[8] M. Morris Mano, Charles Kime. “Logic and computer design fundamentals.” (4th ed.). Pearson, 2014.
[9] Raoelina Andriambololona, “Théorie générale des numérations écrite et parlée". Bull. Acad. Malg. LXIV./1-2, Antananarivo, Madagascar, 1986.
[10] Raoelina Andriambololona, "Théorie générale des numérations écrite et parlée. II Utilisation du calcul matriciel en arithmétique. Nouvelle proposition d’écriture, d’énoncé des règles d’addition et de multiplication des nombres.". Bull. Acad. Malg LXV/1-2, Antananarivo, Madagascar, 1987.
[11] Raoelina Andriambololona, “Théorie générale des numérations écrite et parlée. II- Utilisation du calcul matriciel en arithmétique. Application au changement de bases de numération. Bull. Acad. Malg. LXV./1-2, Antananarivo, Madagascar”, 1987 (1989).
[12] Raoelina Andriambololona, Hanitriarivo Rakotoson “Mpikajy elekronika sy siantifika mampiasa ny fomba fanisana Malagasy (Electronic and scientific calculator based on malagasy counting method)”, communication at the Academie Malgache, Antananarivo Madagascar, 05 June 2008.
Author Information
  • Theoretical Physics Department, Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar

  • Theoretical Physics Department, Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar

  • Theoretical Physics Department, Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar

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  • APA Style

    Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Hanitriarivo Rakotoson. (2016). Numeral System Change in Arithmetic and Matricial Formalism. Pure and Applied Mathematics Journal, 5(3), 87-92. https://doi.org/10.11648/j.pamj.20160503.15

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    ACS Style

    Raoelina Andriambololona; Ravo Tokiniaina Ranaivoson; Hanitriarivo Rakotoson. Numeral System Change in Arithmetic and Matricial Formalism. Pure Appl. Math. J. 2016, 5(3), 87-92. doi: 10.11648/j.pamj.20160503.15

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    AMA Style

    Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Hanitriarivo Rakotoson. Numeral System Change in Arithmetic and Matricial Formalism. Pure Appl Math J. 2016;5(3):87-92. doi: 10.11648/j.pamj.20160503.15

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  • @article{10.11648/j.pamj.20160503.15,
      author = {Raoelina Andriambololona and Ravo Tokiniaina Ranaivoson and Hanitriarivo Rakotoson},
      title = {Numeral System Change in Arithmetic and Matricial Formalism},
      journal = {Pure and Applied Mathematics Journal},
      volume = {5},
      number = {3},
      pages = {87-92},
      doi = {10.11648/j.pamj.20160503.15},
      url = {https://doi.org/10.11648/j.pamj.20160503.15},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.pamj.20160503.15},
      abstract = {The main goal of this paper is to present a method to tackle the numeral system change problem using matricial formalism. In a previous work, we have described an approach which permits to use matricial formalism and matricial calculation in writing numeration and arithmetic. The present paper is focused on the study of the problem of numeral system change in the framework of this approach. The cases of integer numbers and of more general numbers are given.},
     year = {2016}
    }
    

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    AU  - Raoelina Andriambololona
    AU  - Ravo Tokiniaina Ranaivoson
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    JO  - Pure and Applied Mathematics Journal
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    PB  - Science Publishing Group
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    AB  - The main goal of this paper is to present a method to tackle the numeral system change problem using matricial formalism. In a previous work, we have described an approach which permits to use matricial formalism and matricial calculation in writing numeration and arithmetic. The present paper is focused on the study of the problem of numeral system change in the framework of this approach. The cases of integer numbers and of more general numbers are given.
    VL  - 5
    IS  - 3
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