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A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" and "1" ().
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 ...
For example, "11" represents the number eleven in the decimal or base-10 numeral system (today, the most common system globally), the number three in the binary or base-2 numeral system (used in modern computers), and the number two in the unary numeral system (used in tallying scores). The number the numeral represents is called its value.
The binary number system was refined by Gottfried Wilhelm Leibniz (published in 1705) and he also established that by using the binary system, the principles of arithmetic and logic could be joined. Digital logic as we know it was the brain-child of George Boole in the mid 19th century.
Binary function, a function that takes two arguments; Binary operation, a mathematical operation that takes two arguments; Binary relation, a relation involving two elements; Binary-coded decimal, a method for encoding for decimal digits in binary sequences; Finger binary, a system for counting in binary numbers on the fingers of human hands
"Z1 was a machine weighing about 1 tonne in weight, which consisted of some 20,000 parts. It was a programmable computer, based on binary floating-point numbers and a binary switching system. It consisted completely of thin metal sheets, which Zuse and his friends produced using a jigsaw."
Gottfried Wilhelm Leibniz (1646–1716) developed logic in a binary number system and has been called the "founder of computer science". [19] In 1702, Gottfried Wilhelm Leibniz developed logic in a formal, mathematical sense with his writings on the binary numeral system.
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.