Numeral System Change in Arithmetic and Matricial Formalism

Raoelina Andriambololona; Ravo Tokiniaina Ranaivoson; Hanitriarivo Rakotoson

doi:doi:10.11648/j.pamj.20160503.15

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Numeral System Change in Arithmetic and Matricial Formalism

Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Hanitriarivo Rakotoson

Published in Pure and Applied Mathematics Journal (Volume 5, Issue 3)

Received: 12 May 2016 Accepted: 25 May 2016 Published: 7 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.

Published in	Pure and Applied Mathematics Journal (Volume 5, Issue 3)
DOI	10.11648/j.pamj.20160503.15
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), 2016. 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.

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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - Numeral System Change in Arithmetic and Matricial Formalism
AU  - Raoelina Andriambololona
AU  - Ravo Tokiniaina Ranaivoson
AU  - Hanitriarivo Rakotoson
Y1  - 2016/06/07
PY  - 2016
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T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
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VL  - 5
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Author Information

Raoelina Andriambololona

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

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

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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Numeral System Change in Arithmetic and Matricial Formalism
AU  - Raoelina Andriambololona
AU  - Ravo Tokiniaina Ranaivoson
AU  - Hanitriarivo Rakotoson
Y1  - 2016/06/07
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160503.15
DO  - 10.11648/j.pamj.20160503.15
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 87
EP  - 92
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160503.15
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
ER  -

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