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Gottfried Wilhelm Leibniz (or Leibnitz; [a] 1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic and statistics.
The modern binary number system, the basis for binary code, is an invention by Gottfried Leibniz in 1689 and appears in his article Explication de l'Arithmétique Binaire (English: Explanation of the Binary Arithmetic) which uses only the characters 1 and 0, and some remarks on its usefulness. Leibniz's system uses 0 and 1, like the modern ...
He contributed to the theory of linear differential equations and the study of the sum of residues of a rational function. In 1847, Boole developed Boolean algebra, a fundamental concept in binary logic, which laid the groundwork for the algebra of logic tradition and forms the foundation of digital circuit design and modern computer science.
The base-2 numeral system is a positional notation with a radix of 2.Each digit is referred to as a bit, or binary digit.Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because ...
Pingala (roughly 3rd–1st centuries BC) in his treatise of prosody uses a device corresponding to a binary numeral system. [134] [135] His discussion of the combinatorics of meters corresponds to an elementary version of the binomial theorem. Pingala's work also contains the basic ideas of Fibonacci numbers (called mātrāmeru). [136]
Mathematics emerged independently in China by the 11th century BCE. [1] The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system (binary and decimal), algebra, geometry, number theory and trigonometry.
(The largest problem that could be solved without the use of the intermediate output and input was two simultaneous equations, a trivial problem.) Intermediate results were binary, written onto paper sheets by electrostatically modifying the resistance at 1500 locations to represent 30 of the 50-bit numbers (one equation).
It was based on Boolean Algebra and had some of the basic ingredients of modern machines, using the binary system and floating-point arithmetic. Zuse's 1936 patent application (Z23139/GMD Nr. 005/021) also suggested a 'von Neumann' architecture (re-invented about 1945) with program and data modifiable in storage.