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

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