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The History of Computation

The History of Computation. Dr. Sidney Marshall Associate professor Rochester Institute of Technology. Why Do We Calculate? Ancient History. Ancient History Measurement and Surveying - Nile River Astronomy - Predicting Spring Business Records. The Abacus.

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The History of Computation

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  1. The History of Computation Dr. Sidney Marshall Associate professor Rochester Institute of Technology

  2. Why Do We Calculate? Ancient History • Ancient History • Measurement and Surveying - Nile River • Astronomy - Predicting Spring • Business Records

  3. The Abacus • Originally stones on counting board • Chinese "swan pan" in China since 1300 A.D. • Imported as Japanese soroban • In 1946 the best abacus user beat the best electrically driven mechanical calculator in a contest

  4. Chinese Swan Pan

  5. Japanese Soroban

  6. Russian Peasant Multiplication • Only requires doubling and halving • (duplation and mediation)

  7. Multiplication - continued • How to do it • Write the two numbers at top • On successive rows halve the first number and double the second number • Stop when you get to 1 • Cross off every row with an even number in the first column • Add up the remaining numbers in the second column

  8. Multiplication Example: • 21 27 • 10 54 • 5 108 • 2 216 • 1 432 • 567 = 21 x 27

  9. Finger Reckoning • Educated people knew up to 5 x 5 • To multiply two numbers greater than 5: • Extend fingers for amount over 5 • Answer is sum of extended fingers followed by product of "closed" fingers • 7 x 8 = (2+3) and (3 times 2) = 5 6

  10. Tally Sticks • Notched sticks used throughout history for record keeping • Used by English Government for accounts • Sticks were notched and split length-wise into two pieces for each party • Accounts "tallied" by matching sticks

  11. Tally for £11 18s 8d from the reign of Henry III to the Reeve of Ledicumbe Tally Sticks A tally for 6s 8d issued by the Treasurer of Edward I to the Sheriff of Lincolnshire

  12. Tally Stick Fire of 1834 • The order went out that the tally sticks should be burned in a stove in the House of Lords. The stove, overgorged with these preposterous sticks, set fire to the panelling; the panelling set fire to the House of Commons; the two houses of government were reduced to ashes.

  13. Fire caused by burning tally sticks

  14. The Quadrant • A portable analog computer for trigonometrical and astronomical calculations • Calculations were performed using dividers to measure and transfer distances

  15. The Sector • A hinged version of the quadrant • Used for artillery calculations • Calculations could be performed by measuring distances with a divider

  16. Napier's Bones (1550-1617) • Tiles containing a column of the multiplication table

  17. Napier's invention of Logarithms 1614 • Method of prosthaphaeresis • sin a sin b = [cos(a-b) - cos(a+b)]/2 • Using Napier's Logarithms • log ab = log a + log b

  18. Slide Rules • Based on logarithms • Could do multiplication, division, powers, roots, and trigonometric computations • Nearly 3 decimal digits of accuracy • All engineers used to have one

  19. Slide Rule Operation • Adding lengths on a logarithm scale is equivalent to multiplying

  20. Slide Rules

  21. Slide Rules • More accuracy required a longer scale or more accurate mechanism • Many types of slide rules were invented • spiral, cylindrical, long steel tapes, magnifying devices

  22. Cylindrical Slide Rule

  23. Spiral Slide Rule

  24. Graphical computing • planimeters • integrators

  25. The Planimeter

  26. Wilhelm Schickard (1592-1635) • First workable mechanical adding machine

  27. Blaise Pascal (1623-1662) • Several dials like telephone for entering numbers • 9's complement used for subtraction

  28. Mathematical Tables - 1780's • Big effort to produce accurate tables • Powers and roots • Logarithms (addition/subtraction logarithms, quarter squares) • Trigonometric and Exponential tables for geometry • Most scientific calculations carried out with the help of tables

  29. Jacquard's Loom (1752-1834) • Punched cards controlled weaving

  30. Charles Babbage (1791-1871) • Designed many mechanical calculating machines • His "Difference Engine" was designed to calculate tables • Designed the "Analytical Engine" with many of the properties of our modern computers

  31. Method of Differences 0.7242758696 0.0008186515 0.7250945211 -0.0000015403 0.0008171112 0.0000000058 0.7259116323 -0.0000015345 0.0008155767 0.0000000058 0.7267272090 -0.0000015287 0.0008140480 0.0000000057 0.7275412570 -0.0000015230 0.0008125250 0.0000000057 0.7283537820 -0.0000015173 0.0008110077 0.0000000057 0.7291647897 -0.0000015117 0.0008094960 0.7299742857

  32. Babbage's Difference Engine

  33. Babbage's Analytical Engine

  34. Dorr Felt - Comptometer (1886) Designed (out of a macaroni box!) a reliable carrying mechanism

  35. Mechanical Calculating Machines • The 1900's development of many calculators and cash registers • Some were hand powered and some were driven with an electrical motor • Calculators were the workhorse for scientific computation in the 1950’s • A “computer” was a person operating a mechanical calculator

  36. Monroe calculator

  37. Mechanical Differential Analyzers • Vannevar Bush developed the Differential Analyzer - 1930's • All mechanical machine for solving differential equations • Solved the equation dz = y dx • Electrical versions were made later • OP amps and analog computers • Digital differential analyzers

  38. Bush Differential Analyzer

  39. Card Punch equipment • 1880 census results available in 1888 • For the 1890 census Hollerith developed a punched card system • The 1900 census done 1 year 7 months after the results were in

  40. Uses of "Tabulating" Cards • Business records • Subscription cards • Billing • Code Breaking • Atom Bomb Calculations

  41. IBM Card

  42. IBM Punched Card machines

  43. Punch Card Control Panel

  44. The telephone company • Largest distributed relay computer • Specification for telephone office was 1/2 hour outage in 40 years • George Stibitz built a relay computer in 1939 with telephone relays

  45. The "modern" computer era • World War II • Code Breaking • Artillery firing tables • Atom Bomb Calculations

  46. The ENIAC - 1944

  47. The IBM 704 • First "modern" mass produced computer

  48. Storage Technology • Mercury Delay Lines • Williams Storage Tube • Magnetic Core Memory • Semiconductor Memory • The Rule of 4

  49. Core Memory

  50. Off-line Storage • Punched Cards • Paper tape • Magnetic Tape • Magnetic Drum • Magnetic Disk

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