How Computers Work

1. How Computers Work • … and how you can work them. • Art 315 Lecture 03 • Dr. J Parker • Fall 2010

2. What is a Computer? • Thereare many types of computer, but the typical PC or MAC or Linux computer is what we are going to discuss. It is vastly the most common type. • It is referred to as a stored program digital computer (von Neumann machine)

3. Properties of a computer • 1. Computers can only manipulate numbers. • To get a computer to create a picture or music, we must device some sort of code that allows pictures and music to be made into numbers. • This is an encoding, and computers use many of them

4. Computers can only manipulate numbers. • A simple encoding: characters. • On a computer, the letter ‘A’ is stored as the number 65, ‘B’ is 66 … • The number ‘0’ is 48, ‘1’ is 49. and so on. • This is the ASCII (American Standard Code for Information Interchange) code. There are others.

5. ASCII

6. Computers can only manipulate numbers. • Strings are sequences of characters. • E.G. “This is a string” • Is stored as a set of adjacent numbers: • 84 104 105 115 32 105 115 32 97 32 115 116 114 105 110 103 • This is called the representation of the string, and we’ll talk about that sort of thing in the next class.

7. Computers can only manipulate numbers. • Computers can do the following things to numbers: • Add them (and subtract) • Store in memory • Get from memory • Some can multiply/divide • Logical: AND, OR, NOT etc

8. Computers can only manipulate numbers. • Memory is a place where numbers can be stored for later use. • Each place in memory can hold a number. • Each place in memory has an address by which the location is known. To store/retrieve a number in memory one needs and address.

9. Address Memory 1 0 1 2 3 4 5 6 7 8 9 10 2 4 8 16 32 64 128 256 512 1024

10. Accessing memory in a computer • Ask: Give me the contents of location number 8 (address 8). Then it can be changed (EG ‘add to 7’) • Ask: Store 15 into location 8

11. Accessing memory in a computer • Most times one has to get the contents of memory before doing something to it: • Get location 6 (=64) • Get location 5 (=32) • Add them together (=96) • Store result in location 7 • (This is a computer program!)

12. Properties of computers • 2. Computers operate using electricity. • Electronic computers must use some electronic means to store and retrieve numbers. • There must be a way to represent numbers using electricity – voltages, current, etc. • What do you know about electricity?

13. Electricity • Not everyone is good with electricity, so here’s a quick simple summary: • Electricity is a motion of electrons through a conductor. Common analogy is that of water through a pipe. • Water pressure = voltage (difference between the two ends). • Current = amount of water flow (amps) • Resistance = friction with the pipe. (Ohms)

14. Electricity • Electrons have a negative charge. If electrons are like ‘water’ then here is a visual analogy: • -- - - - • - -- - - • - - -- - • - - - - - • - - - - - • - - - - • - ---- • -- - - - Flow is from more electrons to fewer (more ‘negative’ to less ‘negative’ (more ‘positive’)

15. Electricity • For electricity to flow there needs to be a complete loop (unlike water) • Flow is from negative to positive. • Complete loop is a conductor from the –ve pole of the source of electricity to the +ve. + - Arrows show the direction Of electron motion.

16. Electricity • For electricity to flow there needs to be a complete loop (unlike water) • That’s why a switch can turn off a light – it breaks the circuit and there is no longer a loop. + - Arrows show the direction Of electron motion (or not).

17. Electricity • So how can we represent numbers? • Hmm, 10 digits. Maybe 10 voltages? • Leads to complex and slow circuits. ENIAC

18. Properties of computers • 2. Computers use binary numbers, not decimal. • Electronic computers must use some electronic means to store and retrieve numbers, and binary (base 2) is much more effective in electronic circuits. • But what are binary numbers?

19. Binary/Decimal numbers • Grade 3 math coming up … • Our standard number system is Base 10, meaning that there are 10 digits 0, 1, …9 • 10 is the base of the number system, meaning that the representation depends on it. • We probably use 10 as a base because we have 10 fingers

20. Binary/Decimal numbers • The number 342 in base 10 is really • 3 x 100 + 4 x10 + 2 or • 3x102 + 4x101 + 2x100 • The exponent is the digit position, counted right to left starting at 0. • Position 3 2 1 0 • 103=1000 102=100 101=10 100=1 • x x x x • 0 3 4 2 • 300 + 40 + 2 = 342 • 173 = 100 + 70 + 3 = 1x102 + 7x101 + 3x100

21. Binary/Decimal numbers • Why does the base have to be 10? It does not. • How about base 8? • 82 = 64 81 = 8 80=1 • So 342 in base 8 is: • 3x82 + 4x81 + 2x80 or • 3 x 64 + 4 x8 + 2 or • 192 + 32 + 2 = 226 (if it were in base 10) • Base is shown as a subscript: • 342 base 10 is 34210 • 342 base 8 is 3428

22. Binary/Decimal numbers • Numbers always represent the same things • so 1210 means this many: • | | | | | | | | | | | | • 148 = 1210 and means this many: • | | | | | | | | | | | | • The value of the number 12 stays the same, symbolic representation can vary depending on symbols set and base. • Babylonians used base 60!

23. Binary/Decimal numbers • We can do math in much the same way irrespective of base. • Listen carefully:

24. Binary/Decimal numbers • 3 4 2 • - 1 7 3 • Starting at the right do 2-3. • Can’t do that since 2 < 3, so we borrow one (which is 101 = 10) from the next place left. • 12 – 3 = 9 • 3 3 12 • - 1 7 3 • 9

25. Binary/Decimal numbers • 3 32 • - 1 7 3 • Now the next column is 3 - 7. • As before, 3 < 7, so we borrow one (which is 102=100) from the next place left – it was 3, now becomes 2 • 13 – 7 = 6 • 2 13 12 • - 1 7 3 • 6 9

26. Binary/Decimal numbers • 2 32 • - 1 73 • Now the next column is 2 – 1 = 1. • As before, 3 < 7, so we borrow one (which is 102=100) from the next place left – it was 3, now becomes 2 • 13 – 7 = 6 • 2 13 12 • - 1 7 3 • 1 6 9

27. Base 8 (octal) numbers • 3 4 2 • - 1 7 3 • Starting at the right do 2-3. • Can’t do that since 2 < 3, so we borrow one (which is 81 = 810 or 108) from the next place left. • 128 – 38 = 78 • 3 3 12 • - 1 7 3 • 7

28. Base 8 (octal) numbers • 3 32 • - 1 7 3 • Now do 3 - 7. Borrow from the 82 place (64??) • That is, borrow one from the leftmost position, making the 3 into 2 and making the problem 138 – 78. • 138 – 78 = 1110 – 710 = 4 • 3 13 12 • - 1 7 3 • 4 7

29. Base 8 (octal) numbers • 2 32 • - 1 73 • Now do 2 - 1. Still 2 – 1 = 1 • That’s it! the 3 into 2 and making the problem 138 – 78. • So 3428 - 1738 = 1478 • 3 1312 • - 1 73 • 1 47

30. Why Did We Do All Of That? • Because positional number systems like these prevail in most human systems, and in computers too. • In particular, we want to learn about binary (base 2) numbers because computers use binary to store all numbers, all data, all programs. Everything. • The last question asked about 11 slides ago was: • ‘What Are Binary Numbers?’

31. Why Did We Do All Of That? • Binary allows electrical circuits to be simple. Lights, buzzers, toasters, TV sets can be on or off. Two states can be used easily to represent 2 digits: • 0 = OFF • 1 = ON. • So a number can be stored as the settings (states) of a set of switches: • 0 1 1 0 0 1 0 = 50

32. Binary Numbers Are Everything • Everything on a computer is coded as numbers, and all numbers are binary. • Even commands for the computer to execute. • Computers have a memory, a circuit that does calculations, a circuit that controls overall operations, and lots of extra stuff for communications and long term storage.

33. Stored Program Computer • However: • Computers store the commands to be executed (the program) as numbers in its memory. • It fetches the next command (instruction) from memory, then executes it. • This is the fetch-execute cycle.

34. 4. Instructions are Binary Numbers • Principle 4 is: • All Computer Instructions are Binary Numbers. • Instructions in memory can be executed. Those not in memory have to be put there before they can be executed.

35. 4. Instructions are Binary Numbers • Why does this matter? • A good artist (or programmer I guess) needs to be able to have control over their computer. • To be a really good media artist you need to be able to make the machine do what you want (or at least have it make interesting errors)

36. How a computer works - instructions • Load 04 • Here is how the Fetch-execute cycle works 000 001 002 003 004 005 006 007 008 009 010 Here is a sample program in memory. We’ll use decimal at first, and symbolic instructions. Assume that we always start executing a program at memory location 0. • Add 05 • Store 06 • HALT 005 009 000

37. How a computer works - instructions • Load 04 • The address of the instruction changes every time 000 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT 005 009 000 It usually increases by 1. We’ll use a special place to store the address of the next instruction, called the Program counter. It will initially contain 0.

38. How a computer works - instructions • Load 04 • We also need a place where we can do the math 000 000 001 002 003 004 005 006 007 008 009 010 • Add 05 000 • Store 06 • HALT 005 009 000 It’s like the display on a calculator. We’ll call it the accumulator We can add to is, load it, store it, take away from it, etc etc.

39. How a computer works - instructions • We finally need a place to store the instruction • Load 04 • PC IR ACC 000 000 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT … because we increment the program counter. We’ll call it the instruction register OK, now let’s execute. 005 009 000

40. How a computer works - instructions • Load 04 • PC IR ACC 000 Load 004 000 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT FETCH. Get the instruction at the address indicated by the PC. Store it in the IR Add 1 to the PC 005 009 000

41. How a computer works - instructions • Load 04 • PC IR ACC 001 Load 004 000 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT FETCH. Get the instruction at the address indicated by the PC. Store it in the IR Add 1 to the PC 005 009 000

42. How a computer works - instructions • Load 04 • PC IR ACC 001 Load 004 005 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT EXECUTE. Execute the instruction in the IR In this case, Load 4 means: ‘Take the contents of memory location 4 and move a copy of it to the accumulator” 005 009 000

43. How a computer works - instructions • Load 04 • PC IR ACC 001 Add 05 005 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT FETCH. Get the instruction at the address indicated by the PC. Store it in the IR Add 1 to the PC 005 009 000

44. How a computer works - instructions • Load 04 • PC IR ACC 002 Add 05 005 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT FETCH. Get the instruction at the address indicated by the PC. Store it in the IR Add 1 to the PC 005 009 000

45. How a computer works - instructions • Load 04 • PC IR ACC 002 Add 05 014 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT EXECUTE. Execute the instruction in the IR In this case, Add 5 means: ‘Take the contents of memory location 5 and add it to the accumulator” 005 009 000

46. How a computer works - instructions • Load 04 • PC IR ACC 002 Store 06 014 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT FETCH. Get the instruction at the address indicated by the PC. Store it in the IR Add 1 to the PC 005 009 000

47. How a computer works - instructions • Load 04 • PC IR ACC 003 Store 06 014 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT FETCH. Get the instruction at the address indicated by the PC. Store it in the IR Add 1 to the PC 005 009 000

48. How a computer works - instructions • Load 04 • PC IR ACC 003 Srore 06 014 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT EXECUTE. Execute the instruction in the IR In this case, STORE 06 means: ‘Take the contents of the accumulator and store it in memory location 6” 005 009 000

49. How a computer works - instructions • Load 04 • PC IR ACC 003 Srore 06 014 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT EXECUTE. Execute the instruction in the IR In this case, STORE 06 means: ‘Take the contents of the accumulator and store it in memory location 6” 005 009 014

50. How a computer works - instructions • Load 04 • PC IR ACC 003 Halt 014 000 001 002 003 004 005 006 007 008 009 010 • Add 05 • Store 06 • HALT FETCH. Get the instruction at the address indicated by the PC. Store it in the IR Add 1 to the PC 005 009 014