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A binary code represents text or computer processor instructions using the binary number system's two binary digits, 0 and 1. The binary code assigns a bit string to each symbol or instruction. For example, a binary string of eight binary digits (bits) can represent any of 256 possible values and can therefore correspond to a variety of different symbols, letters or instructions. In computing and telecommunications, binary codes are used for various methods of encoding data, such as character strings, into bit strings. Those methods may use fixed-width or variable-width strings. In a fixed-width binary code, each letter, digit, or other character is represented by a bit string of the same length; that bit string, interpreted as a binary number, is usually displayed in code tables in octal, decimal or hexadecimal notation. There are many character sets and many character encodings for them. A bit string, interpreted as a binary number, can be translated into a decimal number. For example, the lower case ''a'', if represented by the bit string 01100001 (as it is in the standard ASCII code), can also be represented as the decimal number 97. ==History of binary code== The modern binary number system, the basis for binary code, was discovered by Gottfried Leibniz in 1679 and appears in his article ''Explication de l'Arithmétique Binaire''. The full title is translated into English as the "Explanation of the binary arithmetic", which uses only the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese figures of Fu Xi."〔Leibniz G., Explication de l'Arithmétique Binaire, Die Mathematische Schriften, ed. C. Gerhardt, Berlin 1879, vol.7, p.223; Engl. transl.()〕 (1703). Leibniz's system uses 0 and 1, like the modern binary numeral system. Leibniz encountered the ''I Ching'' through French Jesuit Joachim Bouvet and noted with fascination how its hexagrams correspond to the binary numbers from 0 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired.〔 Leibniz saw the hexagrams as an affirmation of the universality of his own religious beliefs. Binary numerals were central to Leibniz's theology. He believed that binary numbers were symbolic of the Christian idea of ''creatio ex nihilo'' or creation out of nothing. Leibniz was trying to find a system that converts logic’s verbal statements into a pure mathematical one. After his ideas were ignored, he came across a classic Chinese text called ''I Ching'' or ‘Book of Changes’, which used a type of binary code. The book had confirmed his theory that life could be simplified or reduced down to a series of straightforward propositions. He created a system consisting of rows of zeros and ones. During this time period, Leibniz had not yet found a use for this system.〔(Gottfried Wilhelm Leibniz (1646-1716) )〕 Binary systems predating Leibniz also existed in the ancient world. The aforementioned ''I Ching'' that Leibniz encountered dates from the 9th century BC in China. The binary system of the ''I Ching'', a text for divination, is based on the duality of yin and yang. Slit drums with binary tones are used to encode messages across Africa and Asia.〔 The Indian scholar Pingala (around 5th–2nd centuries BC) developed a binary system for describing prosody in his Chandashutram.〔W. S. Anglin and J. Lambek, ''The Heritage of Thales'', Springer, 1995, ISBN 0-387-94544-X〕 The residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. In the 11th century, scholar and philosopher Shao Yong developed a method for arranging the hexagrams which corresponds, albeit unintentionally, to the sequence 0 to 63, as represented in binary, with yin as 0, yang as 1 and the least significant bit on top. The ordering is also the lexicographical order on sextuples of elements chosen from a two-element set. In 1605, Francis Bacon discussed a system whereby letters of the alphabet could be reduced to sequences of binary digits, which could then be encoded as scarcely visible variations in the font in any random text.〔 Importantly for the general theory of binary encoding, he added that this method could be used with any objects at all: "provided those objects be capable of a twofold difference only; as by Bells, by Trumpets, by Lights and Torches, by the report of Muskets, and any instruments of like nature". Another mathematician and philosopher by the name of George Boole published a paper in 1847 called 'The Mathematical Analysis of Logic' that describes an algebraic system of logic, now known as Boolean algebra. Boole’s system was based on binary, a yes-no, on-off approach that consisted of the three most basic operations: AND, OR, and NOT.〔(What's so logical about boolean algebra? )〕 This system was not put into use until a graduate student from Massachusetts Institute of Technology by the name of Claude Shannon noticed that the Boolean algebra he learned was similar to an electric circuit. Shannon wrote his thesis in 1937, which implemented his findings. Shannon's thesis became a starting point for the use of the binary code in practical applications such as computers, electric circuits, and more.〔(Claude Shannon(1916-2001) )〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Binary code」の詳細全文を読む スポンサード リンク
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