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The binary code

The binary code. T he old chinese tri- and hexagrams of the historical „I Ging“ . Gottfried Wilhelm Leibniz and his D yadi c. And, at the end, the modern ASCII-code . The I-Ging (#1).

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The binary code

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  1. The binary code The old chinese tri- and hexagrams of the historical „I Ging“. Gottfried Wilhelm Leibniz and his Dyadic. And, at the end, the modern ASCII-code.

  2. The I-Ging (#1) • The emergence of the Chinese I-Ging, that is nown as „The book of transformations“, is approximately dated on the 8th century B.C. and is to have been written by several mythical,Chinese kings or emperors.

  3. The I-Ging (#2) • The book represents a system of 64 hexagrams, to which certain characteristics were awarded. • Furthermore it gives late continuously extended appendix, in which these characteristics are interpreted.

  4. The I-Ging (#3) • The pointingnesses and explanations were applied to political decisions and questions of social living together and moral behavior. Even scientific phenomena should be described and explained with the help of these book.

  5. The I-Ging (#4) • A hexagram consists of a combination of two trigrams. • Such a tri gram consists of three horizontal lines, which are drawn either broken in the center or drawn constantly.

  6. The I-Ging (#5) • These linesare to be seen as a binary character. The oppositeness expressed thereby was interpreted laterin the sense of Yin Yang dualism.

  7. The I-Ging (#6) • The 64 possible combinations of the trigrams were brought now with further meanings in connection and arranged according to different criteria. One of the dominantest orders is those of the Fu-Hsi, a mythicalgod-emperor of old China.

  8. The I-Ging (#7) the order of Fu-Hsi

  9. Leibniz and the Dyadic (#1) • That the completely outweighing number of the computers works binary, is today school book wisdom. • But, that the mathematicalybasiswere put exactly 300 years ago, knows perhaps still a few historian and interested mathematicians and/or computer scientists.

  10. Leibniz and the Dyadic (#2) • On 15 March l679 Gottfried Willhelm Leibniz wrote his work with the title „The dyadic system of numbers". • Behind theDyadic of Leibniz hides itselfs nothing less than binary arithmetics, thus the replacement of the common decimal number system by the representation of all numbers only with the numbers 0 and 1.

  11. Leibniz and the Dyadic (#3) the binaries from 0 to16

  12. Leibniz and the Dyadic (#4) • Out of its handwritten manuscript you can take the following description: "I turn into now for multiplication. Here it is again clear that you can‘t imagine anything easier. Because you don‘t need a pythagoreical board (note: a table with squarearrangement of the multiplication table) and this multiplication is the only one, which admits no different multiplication than the already known. You write only the number or, at their place, 0.

  13. Leibniz and the Dyadic (#5) • Approximately half a century stated Leibniz in letters and writings its strong and continuous interest in China. • If this concentrated at first on questions to the language, primarily the special writing language of China, then and deepened it extended lastingly 1689 by the discussions led in Rome with the pater of the Jesuit Order Grimaldi.

  14. Leibniz and the Dyadic (#6) • Thus did developLeibniz‘vision of an up to then unknown culture and knowledge exchange with China: Not the trade with spices and silk against precious metals should shape the relationship with Europe, but a realization exchange in all areas, in theory such as in practice.

  15. The ASCII-code (#1) • The “AmericanStandard Code for Information Interchange“ ASCII was suggested in 1968 on a small letter as standard X3.4-1963 of the ASP and extended version X3.4-1967. • The code specifies a dispatching, in which each sign of latin alphabet and each arabic number corresponds to a clear value.

  16. The ASCII-code (#2) • This standardisation made now information exchange possible between different computer systems. • 128 characters were specified, from which an code length of 7 bits results. • The ASCII-code was taken over of the ISO as an ISO 7-Bit code and registered later in Germany as DIN 66003.

  17. The ASCII-code (#3) • The modern ASCII-code is a modification of the ISO 7-Bit code (in Germany DIN 66003 and/or German Referenzversion/DRV). • It has the word length 7 and codes decimal digits, the characters of the latin alphabet as well as special character. From the 128 possible binary words are 32 pseudo-words and/or control characters.

  18. The ASCII-code (#4) The 7-bit ASCII-code

  19. The ASCII-code (#5) • Later developed extended 8-bit versions of ASCII have 256 characters, in order to code further, partial country dependent special characters. • Unfortunately there are however very different versions, which differ from one to another, what a uniform decoding prevented. • Later developments like the unicode try to include the different alphabets by a larger word length (16 bits, 32 bits).

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