Outline
The History of Computing:
The Early Days
Sector
1598
Avi Yadgar
Gala Yadgar
Abacus
1300
Analytical
Engine
Turing
Harvard
1834
Machine
Mark I
Relay
Difference
1936
1944
1835
Engine 1
Difference
Z3
Harvard
1821
Engine 2
1941
Mark II
Napier’s
Arithmometer
1849
1949
Bones
1820
Comptometer
1617
Stepped
1892
Slide Rule Drum
Differential
1622
1694
Millionaire Analyzer
Curta
1921
Pascaline
1899
1947
1642
Memory
aids
1
Mechanical
calculators
Electromagnetic
General
purpose
2
1300
Abacus
Chinese Abacus
1300
1445
The printing
press Invented
9
9+7
9+7=16
(10-3)
5
1+1+1+1
10+1
•
•
•
•
First record: 14th Century, China
“The first computer”
Still used in Asian countries
Uses: add, subtract, multiply, divide
(-3)
– Fractions and square roots
• 1946 Contest:
– Japanese abacus vs. electric calculator
3
4
http://www.tux.org/~bagleyd/java/AbacusApp.html
O
1598
Sector
1598
Sector
α
100
• Principle:
• Thomas Hood, London 1598
(Galileo, Padua 1592)
• Problems of the time:
– Cannon elevation
– Amount of gun powder
– Drawing, architecture, surveying
5
• Proportions
• Problem:
OA
AB
O' A'
=
A' B'
100
=?
3
27
A
B
O’
• Solution: 100 = X
27
9
α
X
A' B' =
6
AB
3
⇒ X = 100
3
9
A’
B’
1
Sector
1598
• The lines:
Napier’s Bones/Rods
1617
• John Napier,
Scotland 1617
• Multiplication
table
disassembled
– Arithmetic
– Geometric
– Stereometric
– Polygraphic
– Tetragonic
– Metallic
7
8
Napier’s Bones/Rods
1617
1614
Logarithms
• John Napier, Scotland 1614
(Jobst Burgi, Switzerland)
• Principle:
• Uses:
– Multiplication
– Division
– Square roots
log(a × b) = log(a) + log(b)
a
log( ) = log(a ) − log(b)
b
46,785,399 x 7 =
⇒
a × b = 10 log( a )+ log(b )
a
= 10 log( a ) −log(b )
b
• Logarithmic tables
9
10
1622
Slide Rule
• Replaces logarithmic tables
• Gunter's Line of Numbers
1622
Slide Rule - Operations
• Unary functions:
–
–
–
–
–
–
– Edmund Gunter, England
• Slide rule
– William Oughtred, England, 1622
• Precision depends on length
Reciprocals
Square/Square Root
Cube/Cube Root
Common Logarithms
Sines and Cosines
Tangents and Cotangents
• Binary operations:
– Multiplication
– Division
11
12
2
1642
Pascaline
• Blaise Pascal
France, 1642
• Wheels turned
Manually
• Numbers
entered in
sequence
• Cumulative sum
1642
Pascaline - disadvantages
• Too complex
– Only Pascal could repair
• Expensive
– Cost more than replaced people
• Technophobia
– Mathematicians feared for jobs
• Decimal
13
http://perso.orange.fr/therese.eveilleau/pages/truc_mat/textes/pascaline.htm
1694
Stepped Drum
• Design: Gottfried Leibniz, Germany 1694
• Produced: Phillip Hann, Germany 1774
• Commercial: Charles Xavier Thomas, Philippines 1820
15
17
1820
Arithmometer
1829
First mainline
locomotive
16
1820
•
•
•
•
– French currency system was not
14
Arithmometer
Add by one turn of the handle
Multiply by multiple turns of the handle
Subtract and divide by reversing a switch
Disadvantage: “dialing in the digits”
1947
Stepped Drum - Curta
• Developed: Curt Herzstark, Buchenwald, 1940’s
• Produced: Liechtenstein, 1947
• Sold at ~ $120 until 1973
18
3
1947
Stepped Drum - Curta
1947
Stepped Drum - Curta
• Simulator: http://www.vcalc.net/curta_simulator_en.htm
19
20
1887
Felt & Tarrant Comptometer
1887
Comptometer
1876: First long distance
phone call
1879: First cash register
1888: Production of
automobiles
•
•
•
•
Dorr E. Felt, 1887
Produced: 1892-1930
Key driven
Fully automatic carries
21
1887
22
Comptometer
• Improved user interface
1887
• “Software”: instructions for figuring
– multiplication
– subtractions
– division
– square root
– cube root
– interest
– exchange
– discount
* English currency
– Fail-safe keys
• Locked the machine if the operator failed to press
them completely
– Allow multiple keys to be pressed at once
• One per column
• Faster adding
• Multiplication of some numbers
23
Comptometer
24
4
1899
•
•
•
•
Millionaire Calculator
1899
Millionaire Multiplication Table
Invented: Otto Steiger, 1892
Manufactured: Hans W. Egli, Switzerland 1899
Direct multiplication
Also slower
– Addition
– Subtraction
– Division
1897
First radio
station
25
1899
26
Inside The Millionaire
1834
Back to Tables
• Dionysius Lardner’s Cabinet Cyclopaedia
– 40 volumes in 1834, grew up to 134
– 3,700 acknowledged errata
– How many unacknowledged?
• Sources of error:
– Calculation
– Transcription
– Typesetting and printing
27
1821
28
Difference engine
1849
1878
First
phonograph
• Charles Babbage (1791 –1871)
– English mathematician, philosopher, mechanical engineer and
(proto-) computer scientist
• Calculating polynomials with “repeated differences”
– “Complete complex computation”
• Conceived in 1821
• Difference Engine No.2 1847-1849
– Simpler mechanical design
• Calculating polynomials with
“repeated differences”
• nth degree polynomials
– Starting with the nth difference
– Require n registers
• No multiplication
• Example: f ( x) = x 2 + 4
x
F(x)
1
5
2
8
3
13
4
20
1st diff
2nd diff
3
2
5
2
7
2
9
5
2
29
11
6
2
40
13
– Require 2 differences
a0 X n + a1 X n −1 + a2 X n − 2 + ... + an −1 X + an
29
Difference Engine
7
53
2
30
5
1849
Building the engine
• Never built by Babbage
– Lack of funding
– Insufficient manufacturing technology
1853
Building the engine
• 1853 - First full-scale difference engine
• Scheutz (Sweden)
• “Tabulating Machine”
– 15-digit numbers
– 4th-order differences
– Printed output
Casting: cheap but inaccurate
31
1991
32
Building the engine
1991
• 1985 – 1991: Difference Engine No. 2
• The Science Museum in London
– ~4,000 moving parts
– 2.6 tons
– Built to original designs
– Original materials
– Accurate repeat parts
– 31 figures (103 bits)
– 7 differences
3m x 0.7m x 2.5m
33
34
1995
1834
Analytical Engine
• First General Purpose Machine (1834)
– A ‘store’ for holding intermediate results
– A ‘mill’ for arithmetic computations
– Loops
– Conditional branching
– Programmable using punched cards
• Borrowed from weaving looms
• Would have required a steam engine
– But never been built
35
36
6
1834
1834
Analytical Engine
Memory
• Ada Lovelace created
programs for the
Analytical Engine
I/O
Device
Punched
Program
Tape
Memory
Analytical Engine
Store
Data
Memory
Bn =
n!
z dz
2π i v∫ e z − 1 n +1
– Bernoulli numbers
I/O
Device
I/O
Device
µ Controller
ALU
Mill
I/O
Device
CPU
37
1876
Analog Computers
• Physical representation of data
1876
39
1927
1906
Electric washing
machine
Differential Analyzer
• The differential analyzer
– Voltages
– Currents
– Speed of shafts
41
The mill - 1871
38
–
–
–
–
1903
Wright brother’s
first flight
Invented: 1876, James Thomson
Constructed: 1927, MIT
Solves differential equations by integration
Wheel-and-disc mechanisms perform the integration
40
Differential Analyzer
1927
Differential Analyzer
1929
First residential
elevator
42
7
1949
Analog Computers - Moniac
• London, 1949
• Water represent money
• Tanks represent means of
spending money
• Flow represents flow…
1920
The Enigma
• 1920 to the end of WWII
• Electromechanical ciphering machine
• Applies polyalphabetic encryption
– State dependant encoding
• Mechanical and electrical state
– Modeled after financial
models
• Surprisingly accurate…
43
1920
44
The Enigma
1920’s
Household
refrigerators
1890
Punched cards
• Used in the textile industry
• First adaptation by Babbage
– input and data storage
• A competition was held for the US 1890 census
– 1880 US census had taken 7 years to complete
• Winner: Herman Hollerith
– Later founded the Tabulating Machine Company
– Became IBM
• Used mechanical relays to increment mechanical
counters.
• The 1890 census was completed in 6 weeks
45
1928
46
• Specifically-designed layouts
• “General purpose“ at 1928
• Each IBM-style card had 80
characters
– Followed by early terminals
– Last two digits for a year
• 30% of the profit of IBM in 1931
• Use in machines:
– Sorter
– Duplicating Punch
– Collator
47
Punched Tape
Punched cards
• Based on punched cards
– Paper or polyester
– Still being sold (1.5m/KB)
48
8
1835
1835
Relays
• Joseph Henry 1835
• Electronically controlled electrical switch
• A latching relay
– Two relaxed states
(bistable)
– a.k.a 'keep' relays
– Controlled by an electromagnet
– Controls a set of contacts
• With no current the armature and contacts are released
• The coil requires low power
•49 The contacts can switch high powers
1848
b
c
1941
c OUT
0 0
1 1
0 1
1 1
b
0
1
1
0
+V
c
0
51
Konrad Zuse's Z3
1935
First regular
TV broadcast
+V
b or c
b
0
0
1
1
1941
50
Logical Gates by Relays
1848: Boolean
algebra
Electromagnetic Relay
b or c
•
•
•
•
•
•
•
1936: Turing
machine
1941 - First programmable fully automatic machine
2500 relays
Program on punched tape
5 Hz
64 22bits words
Floating point
Based on the mechanical Z1
52
Konrad Zuse's Z3
1944
Harvard Mark I and Mark II
• Built for Harvard by IBM
• Mark I - 1944
– Fully automatic
– Electromagnetic control
– Mechanical counters
– 765K components
– Hundreds KM of wires
– 12m x 2.5m x 0.7m
– 4,500kg
– Mechanical clock
– 72 words
– 23 decimal digits words
53
Z1 – 30,000 moving parts
54
9
Harvard Mark I
1835
55
Harvard Mark I - Front-end
1835
56
1947
Harvard Mark II
• Mark II - 1947
– Electromagnetic components
– Binary representation
– Floating point
– Operation specific hardware
1947
Harvard Mark II
– Complicated programming
• 8 instructions
– 125,000µ s addition
– 750,000 µ s multiplication
Harvard Mark II storage
57
58
????
Bugs
References
•
• What is the origin of the
term “bug”?
•
•
• September 1947
– A moth trapped in a relay
of Mark II
•
Online Museum Exhibits:
– The ENIAC Museum online
http://www.seas.upenn.edu/~museum/index.html
– Computer History Museum, Mountain View, CA
http://www.computerhistory.org/
– The Science Museum, London
http://www.sciencemuseum.org.uk/on-line/babbage/index.asp
– The Computer Museum, System Source
http://www.syssrc.com/html/museum/
– The Museum of HP Calculators
http://www.hpmuseum.org/
– John Wolff's Web Museum
http://home.vicnet.net.au/~wolff/calculators/
– Stephen Johnston’s web pages
http://www.mhs.ox.ac.uk/staff/saj/arithmometer/
“First actual case of bug being found”
• “Bugs” came before computers and computer software
– Thomas Edison,1878
“… and it is then that “bugs” – as such little faults and
difficulties are called – show themselves…”
59
Wikipedia, the free encyclopedia
http://www.wikipedia.org/
S.O.S. MATHematics
http://www.sosmath.com/
Online lecture by Michelle Hoyle
http://lecture.eingang.org/index.html
60
10