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Our First Real System

Our First Real System. Review. On our way to building a computer…. Represent Info with 0’s & 1’s (aka bits). Logic Circuits: Universal Method. 0’s & 1’s. Memory Circuits. Computers. We are here. The System Clock. “500 Mhz Pentium III computer…” What does “500 Mhz” mean?

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Our First Real System

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  1. Our First Real System

  2. Review On our way to building a computer… Represent Info with 0’s & 1’s (aka bits) Logic Circuits: Universal Method 0’s & 1’s Memory Circuits Computers We are here

  3. The System Clock • “500 Mhz Pentium III computer…” • What does “500 Mhz” mean? • It refers to the speed of theSystem Clock.(actually this is only one of the clocks…) • All digital systems have such “Clocks,” even traffic lights and elevator control systems.

  4. Clocks: Some Terminology • Think of System Clock as a heart. • How fast it beats is measured in Hertz (Hz) which means “cycles per second” • Prefixes: • Kilo = 1,000 • Mega = 1,000,000 • Giga = 1,000,000,000

  5. The System Clock (cont.) • Rough idea: System takes a “step” every time the System Clock beats. • We’ll see how this works in an example. • In real life, Clock is a Quartz crystal,which sends out 0’s and 1’s on a wire. • In every cycle, it changes from 0 to 1 and back to 0 0

  6. The System Clock (cont.) • Rough idea: System takes a “step” every time the System Clock beats. • We’ll see how this works in an example. • In real life, Clock is a Quartz crystal,which sends out 0’s and 1’s on a wire. • In every cycle, it changes from 0 to 1 and back to 0 1

  7. The System Clock (cont.) • Rough idea: System takes a “step” every time the System Clock beats. • We’ll see how this works in an example. • In real life, Clock is a Quartz crystal,which sends out 0’s and 1’s on a wire. • In every cycle, it changes from 0 to 1 and back to 0 0

  8. The System Clock (cont.) • Rough idea: System takes a “step” every time the System Clock beats. • We’ll see how this works in an example. • In real life, Clock is a Quartz crystal,which sends out 0’s and 1’s on a wire. • In every cycle, it changes from 0 to 1 and back to 0 1

  9. The System Clock (cont.) • Rough idea: System takes a “step” every time the System Clock beats. • We’ll see how this works in an example. • In real life, Clock is a Quartz crystal,which sends out 0’s and 1’s on a wire. • In every cycle, it changes from 0 to 1 and back to 0 0

  10. The System Clock (cont.) • Rough idea: System takes a “step” every time the System Clock beats. • We’ll see how this works in an example. • In real life, Clock is a Quartz crystal,which sends out 0’s and 1’s on a wire. • In every cycle, it changes from 0 to 1 and back to 0 1

  11. The System Clock (cont.) • Rough idea: System takes a “step” every time the System Clock beats. • We’ll see how this works in an example. • In real life, Clock is a Quartz crystal,which sends out 0’s and 1’s on a wire. • In every cycle, it changes from 0 to 1 and back to 0 0

  12. The System Clock (cont.) • Rough idea: System takes a “step” every time the System Clock beats. • We’ll see how this works in an example. • In real life, Clock is a Quartz crystal,which sends out 0’s and 1’s on a wire. • In every cycle, it changes from 0 to 1 and back to 0 1

  13. The System Clock (cont.) • Rough idea: System takes a “step” every time the System Clock beats. • We’ll see how this works in an example. • In real life, Clock is a Quartz crystal,which sends out 0’s and 1’s on a wire. • In every cycle, it changes from 0 to 1 and back to 0 0

  14. Our System: A Traffic Light

  15. A Traffic Light • Intersection of two one-way roads

  16. A Traffic Light • Intersection of two one-way roads A B Car Sensors

  17. Traffic Light System Clock • Traffic Lights don’t have to act very fast. • Let’s say the System Clock only beatsonce every 4 seconds. • This is 0.25 Hz.(a few Billion times slower than your PC)

  18. Traffic Light Design • How do we go about designing the Traffic Light? • First, let’s think about all the possible States of the traffic light.

  19. Traffic Light • Intersection of two one-way roads A B Car Sensors

  20. Light A Light B

  21. Possible States Light A Light B

  22. Possible States Light A Light B

  23. Possible States Light A Light B

  24. Possible States Light A Light B

  25. Actually Only 4 Possibilities Light A Light B

  26. Traffic Light Design • We figured out some possible States of the Traffic Light. • Next, we should think logically about how the Traffic Light should behave. • For now, we will try to keep it simple. • (Suppose these are infrequently used country roads.)

  27. How should the Light behave? A Light A B Car Sensors Light B

  28. Traffic Light Behavior IF A=1 AND B=0 Light A Light B

  29. Traffic Light Behavior Otherwise IF A=1 AND B=0 Light A Light B

  30. Traffic Light Behavior Otherwise IF A=1 AND B=0 Light A Always Light B

  31. Traffic Light Behavior Otherwise IF A=1 AND B=0 Light A Always IF A=0 AND B=1 Otherwise Light B

  32. Traffic Light Behavior Otherwise IF A=1 AND B=0 Light A Always Always IF A=0 AND B=1 Otherwise Light B

  33. Traffic Light Behavior Otherwise Note:Clock beats every 4 sec.So Light is Yellow for 4 sec. IF A=1 AND B=0 Light A Always Always IF A=0 AND B=1 Otherwise Light B

  34. Traffic Light State Machine Otherwise Note:Clock beats every 4 sec.So Light is Yellow for 4 sec. IF A=1 AND B=0 Light A Always Always IF A=0 AND B=1 Otherwise Light B

  35. Traffic Light Design • We’ve figured out the logical behavior of the Traffic Light in terms of a State Machine: • We know what the states are. • For each state, given any input,we know which state to go to next. • How do we build it?

  36. Traffic Light Design • Thinking this through: • Our machine needs to:

  37. Traffic Light Design • Thinking this through: • Our machine needs to: • Remember which state it is in (Memory)

  38. Traffic Light Design • Thinking this through: • Our machine needs to: • Remember which state it is in (Memory) • Given the state it is in and input values, it must determine which state to go tonext (Logic)

  39. Traffic Light Design • Thinking this through: • Our machine needs to: • Remember which state it is in (Memory) • Given the state it is in and input values, it must determine which state to go tonext (Logic) • And that’s all !

  40. Traffic Light Design • Problem 1: • Remember which state it is in (Memory) • How do represent the states? • We could keep one bit of memory for whether Light A is Green or not, whether it is Yellow or not, … • This would take 6 bits of memory. • There is a much simpler way!

  41. Traffic Light Design • Problem 1: • Remember which state it is in (Memory) • How do represent the states? • Answer: • Just number them (using binary numbers). • We have 4 states. • Call them 00, 01, 10, 11. • We (human designers) will keep track of what these names mean.

  42. Traffic Light States Otherwise IF A=1 AND B=0 Light A Always Always IF A=0 AND B=1 Otherwise Light B

  43. Traffic Light States Otherwise IF A=1 AND B=0 01 00 Light A Always Always IF A=0 AND B=1 11 10 Otherwise Light B

  44. Traffic Light Design • Problem 2: • Given the state it is in and input values, it must determine which state to go tonext (Logic) • Answer:

  45. Traffic Light Design • Problem 2: • Given the state it is in and input values, it must determine which state to go tonext (Logic) • Answer: • Build a Truth Table • Use Universal Method!

  46. M1 M2 ABD1 D2Light A Red Light B Red … Traffic Light Behavior Build A Truth Table for next state / Output

  47. Traffic Light Behavior Otherwise IF A=1 AND B=0 01 00 Light A Always Always IF A=0 AND B=1 11 10 Otherwise Light B

  48. M1 M2 ABD1 D2Light A Red Light B Red … 0 0 1 0 0 1 1 0 Traffic Light Behavior Build A Truth Table for next state / Output

  49. Traffic Light Behavior Otherwise IF A=1 AND B=0 01 00 Light A Always Always IF A=0 AND B=1 11 10 Otherwise Light B

  50. M1 M2 ABD1 D2Light A Red Light B Red … 0 0 1 0 0 1 1 0 0 1 * * 1 0 1 0 Traffic Light Behavior Build A Truth Table for next state / Output

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