1. Our First Real System

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

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

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

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

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

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 beats once 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?
Light A B
Light B
Car
Sensors

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. Light A Light B 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. Light A Light B 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 to next (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 to next (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. Light A Light B Traffic Light States Otherwise IF A=1 AND B=0 Always

43. Light A Light B Traffic Light States 00 01 11 10 Otherwise IF A=1
AND B=0 00 01
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 to next (Logic)
Answer:

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

46. Traffic Light Behavior
Build A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …

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

48. Traffic Light Behavior
Build A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …

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

50. Traffic Light Behavior
Build A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …
0 1 * *

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

52. Traffic Light Behavior
Build A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …
0 1 * *

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

54. Traffic Light Behavior
Build A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …
0 1 * *
1 1 * *

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

56. Traffic Light Behavior
Build A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …
0 1 * *
1 1 * *
… … … … … … …

57. Traffic Light Design
We understand how to represent which state the system is in (so we can store it in Memory)
We understand how the system can determine which state to go to next (Logic)
Let’s put it together…

58. Traffic Light Design
Input: Sensor A
Input: Sensor B

59. Traffic Light Design Current State 2-bit Memory Register Write
Sensor A
Sensor B

60. Traffic Light Design Current State Next 2-bit State Memory Logic
Register
Next
State
Logic
For
Next
State
&
Output
Write
Sensor A
6 Outputs:
for each Light
Sensor B

61. Traffic Light Design Current State 2-bit Memory Logic Register For
Next
State
&
Output
Write
Sensor A
6 Outputs:
for each Light
Sensor B

62. Traffic Light Design Current State 2-bit Memory Logic Register For
Next
State
&
Output
Clock
Sensor A
6 Outputs:
for each Light
Sensor B

63. Design for Any State Machine
Many bits
Current State
Memory
Register
Logic
For
Next
State
&
Output
Clock
Inputs
Outputs

64. State Machines in Real Life
Elevator control systems
Car control systems
VCR’s
Alarm Clocks
Personal Computers
… Just about everything!

65. More Sophisticated Designs
Just add more states, more inputs, more outputs, more rules…
Example: Add a longer delay before Traffic Light changes from Yellow to Red. (Say 8 seconds instead of 4.)

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

67. More Sophisticated Designs
Note that the new “delay” states we added correspond to the SAME combinations of lights as other states (Red/Yellow).
The purpose of the new states is only to add delays.
Logical states need not correspond to different observable states of the machine!

68. More Sophisticated Designs
Can also add other State Machines!

69. More Sophisticated Designs
Example (Fairness):
We might want a separate Timer machine for the Traffic Light:
If cars keep coming, Light should decide after 3 minutes to switch lights.
A Timer is just a state machine that keeps counting beats of the Clock

70. More Sophisticated Designs
Inputs
Outputs
Main State
Machine
Timer
State Machine

71. State Machines that you can program
Next Time:
Computers!
State Machines that you can program