8 October 2013Birkbeck College, U. London1 Introduction to Computer Systems Lecturer: Steve Maybank Department of Computer Science and Information Systems Autumn 2013 Week 2a: History of Computing

8 October 2013Birkbeck College, U. London2 Computing Game Tom has a game in which he pretends to be a computer…

8 October 2013Birkbeck College, U. London3 Equipment A set of boxes Each box has a name: a, b, c, … Each box contains a piece of paper with a single number on it, e.g. box a contains acbde f g

8 October 2013Birkbeck College, U. London4 Instructions Tom carries out instructions such as: Add the number in box a to the number in box c, then put the result in box c, i.e. make the result the new number in box c. Subtract the number in box b from the number in box a. Put the result in box a. Multiply the number in box b with the number in box c. Put the result in box d.

8 October 2013Birkbeck College, U. London5 Observations The computer consists of a memory (the boxes), a device for changing the contents of the memory (Tom) and a list of instructions. The instructions are simple and there are only a few types (so far add, subtract and multiply). The instructions are carried out one at a time. There is no limit to the number of instructions which are carried out (Tom never gets tired).

8 October 2013Birkbeck College, U. London6 Hardware for Evaluating 1+2 Brain Abacus – rods and beads Mechanical – rods and gears Electromechanical – magnets open and close switches Vacuum tubes Transistors and integrated circuits

8 October 2013Birkbeck College, U. London7 Pascals Calculator: the Pascaline Image from Addition and subtraction only. For an illuminating moving example (in French – click on GO) see

8 October 2013Birkbeck College, U. London8 Difference Engine Early computer for squaring numbers, and much more. Numerical results printed out in the form of tables. Designer: Charles Babbage ( ) 1821: plans for a Difference Engine. 1832: partially built by Joseph Clement. 1834: plans for a more advanced computer, the programmable Analytical Engine. Never built. See

Calculation of Squares Using Differences xx*x1 st difference2 nd difference October 2013Brookshear Section 0.29

8 October 2013Birkbeck College, U. London10 Difference Engine Engine constructed from Babbages designs by the Science Museum

8 October 2013Birkbeck College, U. London11 Lego® Version of the Difference Engine Built by Andrew Carol

8 October 2013Birkbeck College, U. London12 Electromechanical Computer 1 st fully automatic computer. Vol16x2.4x0.6 m 3, weight 4500 Kg. Instructions read from punched paper. Store: 72 nums. of 23 dec. digits. Speed: + or s., * 6 s., / 15.3 s. H. Aiken, 1944

8 October 2013Birkbeck College, U. London13 ENIAC 18,000 vacuum tubes Vol 30x2.4x0.9 m 3, Weight Kg Data input: card reader. Volatile store: twenty 10 digit decimal nos. Read only store: 100 nos. Programming: rewire Speed: + or – 0.2 ms, * 3 ms, / 25 ms. J. Presper-Eckert and J. Mauchley

8 October 2013Birkbeck College, U. London14 Computing at Birkbeck 1945: Andrew Booth recruited by J.D. Bernal to work on mathematical methods for inferring crystal structure from X-rays : builds series of computers, Automatic Relay Computer (ARC), ARC2, SEC, … 1957: establishes Department of Numerical Automation at Birkbeck See

8 October 2013Birkbeck College, U. London15 Computing at Birkbeck MSc student Norman Kitz working on the SEC (Simple Electronic Computer) at Birkbeck (1949). 50years/50yearsofcomputing.pdf

8 October 2013Birkbeck College, U. London16 Algorithms An algorithm is an ordered set of unambiguous executable steps that defines a terminating process. It is implicit that something (e.g. a machine) carries out the steps.

8 October 2013Birkbeck College, U. London17 Informal Algorithms Directions to go from one place to another. Cooking recipes. How to use a device (TV, microwave, etc.) How to assemble flat pack furniture A list of instructions for Tom

8 October 2013Birkbeck College, U. London18 Algorithms and Computers An algorithms is converted into a list of instructions (program) for a particular computer. The details of the instructions vary from one computer to another If an algorithm is programmable on one computer, then it is programmable on any computer.

8 October 2013Birkbeck College, U. London19 First Example of an Algorithm Input: integers 12, 5 Output: quotient q and remainder r on dividing 12 by 5 Algorithm 1. q = 0; r = 12; 2. Subtract 5 from r; Increase q by 1; 3. Subtract 5 from r; Increase q by 1; 4. Output q, r; 5. Halt;

8 October 2013Birkbeck College, U. London20 Second Example of an Algorithm Input: strictly positive integers m, n Output: quotient q and remainder r on dividing m by n Algorithm 1. q = 0; 2. r = m; 3. If r < n, Output q, r; Halt; 4. r = r-n; 5. q = q+1; 6. go to 3;

8 October 2013Birkbeck College, U. London21 Third Example of an Algorithm Input: strictly positive integers m, n Output: quotient q and remainder r on dividing m by n Algorithm 1. q = 0; 2. r = m; 3. While r >= n, 4. r = r-n; 5. q = q+1; 6. EndWhile 7. Output q, r; 8. Halt;

8 October 2013Birkbeck College, U. London22 Exercise Sketch an algorithm that takes as input a strictly positive integer n and outputs an integer k such that