presentation main seminar „didactics of computer science“ version: 2003-02-27 binary coding:...
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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
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.
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.
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 most dominant 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 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.
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).
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.
Counting soldiers
Mutation of grooves and stones
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.
Roman abacus
Calculating on tables
This structure was found on tables, boards and on kerchiefs.
Gelosia procedure of writing calculation
1 2 30
8
5
6
440 1
21
050 1
51
260 1
8
0 8 8
5
6
0
56008123 · 456 =
Napier Bones
50
60
70
80
90
10
20
30
40
1
01
21
41
61
81
20
40
60
80
2
51
81
12
42
72
30
60
90
21
3
54
45
36
27
18
90
81
72
63
9
Calculating with Napier Bones
01
21
41
61
81
20
40
60
80
2
51
81
12
42
72
30
60
90
21
3
54
45
36
27
18
90
81
72
63
9
239 · 8 = 2191
Gottfried Wilhelm Leibniz(1646-1716)
http://www.ualberta.co/~nfriesen/582/enlight.htm
A presentation by Kati Radloff27.02.2003
Leibniz‘ Fields of Interest
Mathematics Physics
Philosophy
Leibniz‘ Father
-died, when Leibniz was six years of age.
- Leibniz‘ mother followed him a couple of years later
Nikolai-School
http://www.genetalogie.de/gallery/leib/leibhtml/leib1a.html
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.
The University of Altdorf
http://www.genetalogie.de/gallery/leib/leibhtml/leib2.html
Here, Leibniz graduated after 6 years of intense studying with a doctor‘s degree and a habilitation at the age of 20.
Leibniz was offered a place to work as professor, but refused to become politically active.
Leibniz‘ mathematical discoveries
http://www.awf.musin.de/comenius/4_3_tangent.html
Infinitesimal calculus
Determinant calculus
Binary System
Leibniz‘ mathematical discoveries
Infinitesimal calculus
Determinant calculus
Binary arithmetics
Mathematics Physics
Philosophy
Leibniz‘ Correspondences
http://www.awg.musin.de/comenius/4_4_correspondence_e.html
Among his 60000 pieces of writing are extensive correspondences, e.g. with mathematicians from China and Vietnam.
Leibniz‘ Intersubjectivity(1)
Infinitesimal calculus
Determinant calculus
Binary arithmetics
Binary machine
theodizee
Mathematics Physics
Philosophy
„One created everything out of nothing“
http;//pauillac.inria.fr/cidigbet/web.html
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.
Leibniz‘ Achievements
Infinitesimal calculus
Determinant calculus
Binary arithmetics
The term of „function“
monadology
Binary machine
Calculator
theodizee
Mathematics Physics
Philosophy
Relativity theory
Sentence of energy maintenance
Continuity principle
Binary Machine and Calculator
Binary machine
Calculator
Gottfried Wilhelm Leibniz and his calculating machine
report by Torsten Brandes
Chapter 1
• Construction of mechanical calculating machines
Structure of a mechanical calculating machine• counting mechanism
two counting wheels
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.
counting mechanism
dealing with the carry between two digits
S – leverZi – toothed wheel
Chapter 2: calculating machines bevore and after Leibniz
• 1623Wilhelm Schickard developes a calculating machine for all the four basic arithmetic operations. It helped Johann Kepler to calculate planet‘s orbits.
• 1641Blaise Pascal developes an adding- and subtracting machine to maintain his father, who worked as a taxman.
• 1670 - 1700 Leibniz is working on his calculator.
• 1774Philipp Matthäus Hahn (1739-1790) contructed the first solid machine.
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.
stepped drumA configuration of staggered teeth. The toothed wheel can be turned 0 to 9 teeth, depending of the position of this wheel.
four basic operations performing machine by Leibniz
Skizze
• H – crank• K – crank for arithmetic shift• rotation counter
drawing: W. Jordan
Functionality
• Addition:
partitioning in two tacts
1. Addition digit by digit, saving the occuring carries with a toothed wheel.
2. Adding the saved carries to the given sums, calculated before.
Subtraction.
• Similar to adding.
• The orientation of rotating the crank has to be turned.
Multiplication (excampel)• was possible by interated additions• 32.448*751. Input of 32.448 in the adjusting mechanism.2. Input of 5 in the rotation counter.3. Rotating the crank H once. The counting mechanism
shows 162.240.4. Rotating the crank K. The adjusting mechanism is
shifted one digit left.5. Input of 7 in the rotation counter.6. Rotating the crank H once. The counting mechanism
shows 2.433.600.
Charles Babbage (1791 - 1871)
• born: 12/26/1791
• son of a London banker
• Trinity College, Cambridge
• Lucasian Professorship
• Mathematician and Scientist
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
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
• 1834 plans for an improved device, capable of calculating any mathematical function
• increase of calculating speed
• never completed
Analytical Engine
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
• 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
Analytical Engine
Analytical Engine
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
Babbage’s meaning in history
• John von Neumann (1903 - 1957): universal computing machine consisting of:– memory – input / output – arithmetic/logic unit (ALU)– control unit
• based on Babbage‘s ideas
• 95 % of modern computers are based on the von Neumann architecture
Babbage’s 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
A Mechanical Revolution of Computing: Hollerith-Machines
(Joerg Dieckmann)
Who was Hermann Hollerith?
• H. Hollerith was an engineer and inventor.
• he lived in the USA• he constructed
machines between 1890-1930
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)
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, …)
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)
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
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.
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.
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.