The binary code

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 lines are to be seen as a binary character.
  The oppositeness expressed thereby was
  interpreted later in 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 mythical god-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 mathematicaly basis were 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 the Dyadic 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.

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Leibniz and the Dyadic (3)

• the binaries from 0 to16

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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
  cant imagine anything easier. Because you dont
  need a pythagoreical board (note a table with
  square arrangement 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 develop Leibniz 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.

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The ASCII-code (1)

• The American Standard 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.

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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.

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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

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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).