Presentation Main Seminar

1
PresentationMain Seminar Didactics of Computer
Science

• Version 2003-02-27
• Binary Coding Alex Wagenknecht
• Abacus Christian Simon
• Leibniz (general) Katrin Radloff
• Leibniz (calculating machine) Torsten Brandes
• Babbage Anja Jentzsch
• Hollerith Jörg Dieckmann

2
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.
3
The I-Ging (1)

• The emergence of the Chinese I-Ging, that is
  known 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.

4
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.

5
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.

6
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.

7
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.

8
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 most dominant orders is those of the
  Fu-Hsi, a mythical god-emperor of old China.

9
The I-Ging (7)

• the order of Fu-Hsi

10
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.

11
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.

12
Leibniz and the Dyadic (3)

• the binaries from 0 to16

13
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.

14
Leibniz and the Dyadic (5)

• Approximately half a century Leibniz stated 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.

15
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.

16
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.

17
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.

18
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.

19
The ASCII-code (4)

• The 7-bit ASCII-code

20
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).

21
History of abacus
The abacus' history started ca. 2600 years ago in
Madagaskar. There to count the amount of
soldiers, every soldier had to pass a narrow
passage. For each passing soldier a little stone
was put into a groove. When ten stones were in
that groove they were removed and one stone was
put into the next groove.
22
Counting soldiers
23
Mutation of grooves and stones
24
Development of soroban
In 607 the japanese regent Shotoku Taishi made a
cultural approach to China. The chinese suan-pan
comes to Japan and became optimized by Taishi by
removing one of the upper balls. Since 1940 the
new soroban with only four lower balls is used.
25
Roman abacus
26
Calculating on tables
This structure was found on tables, boards and on
kerchiefs.
27
Gelosia procedure of writing calculation
0
5
6
0
8
8
56008
123 456
28
Napier Bones
29
Calculating with Napier Bones
239 8
2
1
9
1
30
Gottfried Wilhelm Leibniz(1646-1716)
http//www.ualberta.co/nfriesen/582/enlight.htm
A presentation by Kati Radloff 27.02.2003 radlo
ff_at_inf.fu-berlin.de
31
Leibniz Fields of Interest
Mathematics
Physics
Philosophy
32
Leibniz Father

• died, when Leibniz was six years of age.
• Leibniz mother followed him a couple of years
  later

33
Nikolai-School
Leibniz taught himself Latin at the age of 8. He
graduated from this high school at 14 years of
age as one of the best students. He then
attended the philosophical and juridical faculty
of the University of Altdorf.
http//www.genetalogie.de/gallery/leib/leibhtml/le
ib1a.html
34
The University of Altdorf
Here, Leibniz graduated after 6 years of intense
studying with a doctors degree and a
habilitation at the age of 20.
http//www.genetalogie.de/gallery/leib/leibhtml/le
ib2.html
Leibniz was offered a place to work as professor,
but refused to become politically active.
35
Leibniz mathematical discoveries
http//www.awf.musin.de/comenius/4_3_tangent.html
Infinitesimal calculus
Determinant calculus
Binary System
36
Leibniz mathematical discoveries
Mathematics
Physics
Infinitesimal calculus
Determinant calculus
Binary arithmetics
Philosophy
37
Leibniz Correspondences
Among his 60000 pieces of writing are extensive
correspondences, e.g. with mathematicians from
China and Vietnam.
http//www.awg.musin.de/comenius/4_4_correspondenc
e_e.html
38
Leibniz Intersubjectivity(1)
Mathematics
Physics
Infinitesimal calculus
Binary machine
Determinant calculus
Binary arithmetics
theodizee
Philosophy
39
One created everything out of nothing
Just as the whole of mathematics was constructed
from 0 and 1, so the whole universe was generated
of the pure being of God and nothingness.
http//pauillac.inria.fr/cidigbet/web.html
40
Leibniz Achievements
Mathematics
Physics
Infinitesimal calculus
Relativity theory
Binary machine
Determinant calculus
Sentence of energy maintenance
Calculator
Binary arithmetics
Continuity principle
The term of function
theodizee
monadology
Philosophy
41
Binary Machine and Calculator
Binary machine
Calculator
42
Gottfried Wilhelm Leibniz and his calculating
machine

• report by Torsten Brandes

43
Chapter 1

• Construction of mechanical calculating machines

44
Structure of a mechanical calculating machine

• counting mechanism

two counting wheels
45
counting mechanism

• Every counting wheel represents a digit.
• By rotating in positive direction it is able to
  add, by rotating in negative direction it is able
  to subtract.
• If the capacity of a digit is exceeded, a carry
  occurs.
• The carry has to be handed over the next digit.

46
counting mechanism
S lever Zi toothed wheel
dealing with the carry between two digits
47
Chapter 2 calculating machines bevore and after
Leibniz

• 1623
• Wilhelm Schickard developes a calculating machine
  for all the four basic
• arithmetic operations. It helped Johann Kepler to
  calculate planets orbits.
• 1641
• Blaise Pascal developes an adding- and
  subtracting machine to maintain
• his father, who worked as a taxman.
• 1670 - 1700
• Leibniz is working on his calculator. 
• 1774
• Philipp Matthäus Hahn (1739-1790) contructed the
  first solid machine.

48
Leibniz calculating machine.

• Leibniz began in the 1670 to deal with the topic.
• He intended to construct a machine which could
  perform the four basic arithmetic operations
  automatically.
• There where four machines at all. One (the last
  one) is preserved.

49
stepped drum
A configuration of staggered teeth. The toothed
wheel can be turned 0 to 9 teeth, depending of
the position of this wheel.
50
four basic operations performing machine by
Leibniz
51
Skizze
drawing W. Jordan

• H crank
• K crank for arithmetic shift
• rotation counter

52
Functionality

• Addition
• partitioning in two tacts
• Addition digit by digit, saving the occuring
  carries with a toothed wheel.
• Adding the saved carries to the given sums,
  calculated before.

53
(No Transcript)
54
Subtraction.

• Similar to adding.
• The orientation of rotating the crank has to be
  turned.

55
(No Transcript)
56
Multiplication (excampel)

• was possible by interated additions
• 32.44875
• Input of 32.448 in the adjusting mechanism.
• Input of 5 in the rotation counter.
• Rotating the crank H once. The counting mechanism
  shows 162.240.
• Rotating the crank K. The adjusting mechanism is
  shifted one digit left.
• Input of 7 in the rotation counter.
• Rotating the crank H once. The counting mechanism
  shows 2.433.600.

57
The father of computing historyCharles Babbage
by Anja Jentzsch jentzsch_at_inf.fu-berlin.de
58
Charles Babbage (1791 - 1871)

• born 12/26/1791
• son of a London banker
• Trinity College, Cambridge
• Lucasian Professorship
• Mathematician and Scientist

59
Difference Engine

• 1822 plan for calculating and printing
  mathematical tables like they were used in the
  navy
• using the method of difference, based on
  polynomial functions

60
Difference Engine

• 1822 design 6 decimal places with second-order
  difference
• 1830 engine with 20 decimal places and a
  sixth-order difference
• 1830 end of work on the difference engine because
  of a dispute with his chief engineer

61
Analytical Engine

• 1834 plans for an improved device, capable of
  calculating any mathematical function
• increase of calculating
• speed
• never completed

62
Analytical Engine - Architecture

• separation of storage and calculation
• store
• mill
• control of operations by microprogram
• control barrels
• user program control using punched cards
• operations cards
• variable cards
• number cards

63

Analytical Engine

• more than 200 columns of gear trains and number
  wheels
• 16 column register (store 2 numbers)
• 50 register columns, with 40 decimal digits of
  precision
• counting apparatus to keep track of repetitions
• cycle time 2.5 seconds to transfer a number from
  the store to a register in the mill
• addition 3 seconds
• conditional statements

64

Analytical Engine
65
First programmer Ada Lovelace

• Ada Lady Lovelace, daughter of Lord Byron, was
  working with Babbage on the Analytical Engine
• first ideas of
• algorithm representation
• programming languages
• already realized
• program loops
• conditional statements

66
Babbages meaning in history

• John von Neumann (1903 - 1957) universal
  computing machine consisting of
• memory
• input / output
• arithmetic/logic unit (ALU)
• control unit
• based on Babbages ideas
• 95 of modern computers are based on the von
  Neumann architecture

67
Babbages meaning in history

• Howard Aiken (1900 1973) developed the ASCC
  computer (Automatic Sequence Controlled
  Calculator)
• could carry out five operations, addition,
  subtraction, multiplication, division and
  reference to previous results
• Aiken was much influenced by Babbage's writings
• he saw the ASCC computer as completing the task
  which Babbage had set out on but failed to
  complete

68
A Mechanical Revolution of Computing
Hollerith-Machines
(Joerg Dieckmann)
69
Who was Hermann Hollerith?

• H. Hollerith was an engineer and inventor.
• he lived in the USA
• he constructed machines between 1890-1930

70
Why did he build machines?

• The U.S. government counts the people living in
  the USA every 10 years (census).
• H. Hollerith wanted to make the counting of the
  people easier.
• (below, you can see a table used for counting by
  hand)

71
What was his idea?

• Hollerith took one paper card for each person and
  made holes in it (punched cards)
• The positions of the holes described the person
  (male, fe-male, age, )

72
What did the machines do?

• The Hollerith-Machines counted each item on a
  card.
• They were much faster than people working on
  paper.
• (In the Picture, you see the clocks for
  counting)

73
How did the machines work?

• Each card was placed in a press.
• If there was a hole in the card, an electrical
  circuit was closed and the clocks counted the
  hole.

Card
74
What was the influence of these machines?

• Holleriths and other machines working with
  punched cards were used in Europe and the USA
  from 1900 until 1960.
• The first machines of IBM were like this.
• Later machines could also do sorting and
  arithmetic with punched cards.

75
Who used the machines?

• The USA, Russia and England did their censuses
  (countings of the population) with
  Hollerith-Machines,
• The german Nazi government under Hitler used
  them, IBM helped them with it.

76
Conclusion

• The techniques used were very simple.
• Hollerith was the first, who processed really big
  amounts of data.
• After the introduction of his machines, people
  had to worry about the consequences of computers
  for their life.