Journal of Mahani Mathematical Research

Journal of Mahani Mathematical Research

The evolution of binary system from predynastic Egypt to Leibniz era

Document Type : Special Issue Dedicated to Prof. Esfandiar Eslami

Authors
Z. Pourfereidouni 1
M. Radjabalipour 2, 3
1 Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran
2 Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
3 Pardis Research Group in Technology and Applied Mathematics, Kerman, Iran
10.22103/jmmr.2024.23178.1606
Abstract
Egyptians of the predynastic era had a good decimal number system for counting and addition. Although, up to some times, they had problem in counting beyond a million, by the dawn of their history, Narmer, the founder of the first Egyptian dynasty had accountants that could record 400,000 cows and 1,422,000 goats of a war booty. Except for some ambiguities in the case of Mayan number system, specialists in the history of mathematics can guess that  how the counting system of the various civilizations evolved into one of the number systems in base 10, 20, 60, etc. There is a puzzle in the mixture of the  Egyptian decimal and binary number systems which we are going to discuss and present a justification for it. The novelty of the present paper is the study of the evolution of the binary number system from the predynastic Egypt down to the Leibniz era who, by the benefit of  Khwarazmi's  "Indian Arithmetics,"  completed this evolution by representing integers in $0-1$ forms and performing the hybrid decimal/binary Egyptian arithmetic operations purely inside the $0-1$ system. The second author is pleased to dedicate his share of this paper to  Esfandiar Eslami  showing  his love and appreciation for decades of his friendship and collaboration (since 1967) and, of course, the young coauthor joins the joy of this dedication to her former professor.
Keywords
Egyptian fractions
Binary systems
Binary logic
Zero-one
Subjects
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Journal of Mahani Mathematical Research
Volume 13, Issue 4 - Serial Number 29
Special issue dedicated to Professor Esfandiar Eslami ( To introduce Professor Esfandiar Eslami, please visit: https://jmmrc.uk.ac.ir/p_esfandiareslami ) ( Guest Editors: Prof. R. A. Borzooei, Prof. B. Davvaz, Prof. M. Golshani, Prof. M. Moniri )
December 2024
Pages 1-20

  • Receive Date 03 April 2024
  • Accept Date 05 June 2024