Transcript Document

Presentation
Main 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 ASCIIcode.
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 FuHsi, 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
0
3
0
0
1
4
0
8
1
5
0
1
6
5
5
8
6
1
6
0
4
1
5
0
2
2
8
8
123 · 456 =
56008
Napier Bones
1
0
2
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
6
3
7
4
2
8
4
6
2
1
9
5
2
1
5
8
4
8
4
1
1
6
5
2
7
3
1
1
7
2
0
6
2
1
1
8
9
8
5
1
0
0
9
6
6
4
0
3
4
3
9
2
8
7
1
Calculating with Napier Bones
2
3
0
9
0
2
0
0
3
0
4
0
1
6
0
6
0
9
8
2
0
5
2
8
4
1
6
3
7
4
2
8
4
6
2
1
5
5
2
1
6
4
1
1
7
3
1
1
8
2
1
1
9
2
8
7
1
239 · 8 = 1912
Gottfried Wilhelm Leibniz
(1646-1716)
http://www.ualberta.co/~nfriesen/582
/enlight.htm
A presentation by Kati Radloff
[email protected]
27.02.2003
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
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.
http://www.genetalogie.de/gallery/leib/leibhtml/leib1a.html
He then attended the
philosophical and
juridical faculty of the
University of Altdorf.
The University of Altdorf
Here, Leibniz graduated
after 6 years of intense
studying with a doctor‘s
degree and a habilitation
at the age of 20.
http://www.genetalogie.de/gallery/leib/leibhtml/leib2.html
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
Mathematics
Physics
Infinitesimal
calculus
Determinant
calculus
Binary
arithmetics
Philosophy
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_correspondence_e.html
Leibniz‘ Intersubjectivity(1)
Mathematics
Physics
Infinitesimal
calculus
Determinant
calculus
Binary
machine
Binary
arithmetics
theodizee
Philosophy
„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
Leibniz‘ Achievements
Mathematics
Physics
Infinitesimal
calculus
Determinant
calculus
Binary
arithmetics
Binary
machine
Relativity
theory
Sentence of energy
maintenance
Calculator
Continuity
principle
The term of
„function“
theodizee
monadology
Philosophy
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
S – lever
Zi – toothed wheel
dealing with the carry between two digits
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 planet‘s 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.
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 drum
A 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
drawing: W. Jordan
• H – crank
• K – crank for arithmetic shift
• rotation counter
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)
•
•
1.
2.
3.
4.
5.
6.
was possible by interated additions
32.448*75
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.
The father of computing history:
Charles Babbage
by Anja Jentzsch
[email protected]
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 secondorder 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
Analytical Engine
• 1834
plans for an improved device,
capable of calculating any mathematical
function
• increase of calculating
speed
• never completed
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
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
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, female, age,
…)
What did the machines do?
• The „HollerithMachines“
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.