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ABSTRACT:
This paper discusses the formalization of the binary number system and the groundwork that was laid for the future of digital circuitry, computers, and the field of computer science. The goal of this paper is to show how Gottfried Leibniz formalized the binary number system and solidified his thoughts through an analysis of the Chinese I Ching. In addition, Leibniz's work in logic and with computing machines is presented. This work laid the foundation for Boolean algebra and digital circuitry which was continued by George Boole, Augustus De Morgan, and Claude Shannon in the centuries following. Some have coined Leibniz the world's first computer scientist, and this paper will attempt to demonstrate a validation of this conjecture.
Keywords: binary number system, Boolean logic, Gottfried Leibniz, I Ching, hexagram, trigram
1 Introduction
The binary number system is one of the most influential developments in the history of technology. The formalization of the system and its additions and refinements over the course of 200+ years ultimately led to the creation of electronic circuitry constructed using logic gates. This creation ushered in the technological era and left the world forever changed. Important figures in the history of the binary number system and mathematical logic and less directly the history of computers and computer science include Gottfried Leibniz, George Boole, Augustus De Morgan and Claude Shannon. This paper focuses on Leibniz's formalization of the binary system and his work in mathematical logic and computing machines.
2 Numeric Systems
In the most general sense, a number is an object used to count, label, and measure (Nechaev, 2013). In tum, a numeral or number system is a system for expressing numbers in writing. In the history of mathematics, many different number systems have been developed and used in practice. The most common system currently in use is the Hindu-Arabic numeral system, which was developed between the 1st and 4th centuries and later spread to the western world during the Middle Ages (Smith & Karpinski, 1911). The Hindu-Arabic system is based on ten different symbols and is considered to be a base 10 system. Numeral systems with different bases have found use in applications where a different base provides certain advantages.
Other numeral systems currently in use include the...