Transcript Document

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 ASCIIcode.
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.
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.
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.
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.
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.
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.
The I-Ging (#7)
the order of Fu-Hsi
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.
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.
Leibniz and the Dyadic (#3)
the binaries from 0 to16
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 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.
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.
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.
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.
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.
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.
The ASCII-code (#4)
The 7-bit ASCII-code
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).