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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? - PowerPoint PPT Presentation
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Our First Real System
ReviewOn our way to building a computer…
Computers
We are here
LogicCircuits:UniversalMethod
0’s&1’s
RepresentInfo with0’s & 1’s(aka bits)
MemoryCircuits
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.
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
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
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
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
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
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
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
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
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
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
Our System:A Traffic Light
A Traffic Light
• Intersection of two one-way roads
A Traffic Light
• Intersection of two one-way roads
CarSensors
B
A
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)
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.
Traffic Light
• Intersection of two one-way roads
CarSensors
B
A
Light
A
Light B
Light
A
Light B
Possible States
Light
A
Light B
Possible States
Light
A
Light B
Possible States
Light
A
Light B
Possible States
Light
A
Light B
Actually Only 4 Possibilities
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.)
Lig
ht
A
Light B
How should the Light behave?
CarSensors
B
A
Light
A
Light B
Traffic Light Behavior
IF A=1
AND B=0
Light
ATraffic Light Behavior
IF A=1
AND B=0
Otherwise
Light B
Light
ATraffic Light Behavior
IF A=1
AND B=0
Always
Otherwise
Light B
Light
ATraffic Light Behavior
IF A=1
AND B=0
Always
Otherwise
Light BOtherwise
IF A=0
AND B=1
Light
ATraffic Light Behavior
IF A=1
AND B=0
Always
IF A=0
AND B=1
Otherwise
Light BOtherwise
Always
Light
ATraffic Light Behavior
IF A=1
AND B=0
Always
IF A=0
AND B=1
Otherwise
Light BOtherwise
Always
Note:Clock beatsevery 4 sec.So Light is Yellow for
4 sec.
Light
ATraffic Light State Machine
IF A=1
AND B=0
Always
IF A=0
AND B=1
Otherwise
Light BOtherwise
Always
Note:Clock beatsevery 4 sec.So Light is Yellow for
4 sec.
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?
Traffic Light Design
• Thinking this through:
• Our machine needs to:
Traffic Light Design
• Thinking this through:
• Our machine needs to:
• Remember which state it is in (Memory)
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)
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 !
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!
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.
Light
ATraffic Light States
IF A=1
AND B=0
Always
IF A=0
AND B=1
Otherwise
Light BOtherwise
Always
Light
ATraffic Light States
IF A=1
AND B=0
Always
IF A=0
AND B=1
Otherwise
Light BOtherwise
Always
00 01
1011
Traffic Light Design
• Problem 2:
• Given the state it is in and input values, it must determine which state to go tonext (Logic)
• Answer:
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!
Traffic Light BehaviorBuild A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …
Light
ATraffic Light Behavior
IF A=1
AND B=0
Always
IF A=0
AND B=1
Otherwise
Light BOtherwise
Always
00 01
1011
Traffic Light BehaviorBuild A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …
0 0 1 0 0 1 1 0
Light
ATraffic Light Behavior
IF A=1
AND B=0
Always
IF A=0
AND B=1
Otherwise
Light BOtherwise
Always
00 01
1011
Traffic Light BehaviorBuild A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …
0 0 1 0 0 1 1 0
0 1 * * 1 0 1 0
Light
ATraffic Light Behavior
IF A=1
AND B=0
Always
IF A=0
AND B=1
Otherwise
Light BOtherwise
Always
00 01
1011
Traffic Light BehaviorBuild A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …
0 0 1 0 0 1 1 0
0 1 * * 1 0 1 0
1 0 0 1 1 1 0 1
Light
ATraffic Light Behavior
IF A=1
AND B=0
Always
IF A=0
AND B=1
Otherwise
Light BOtherwise
Always
00 01
1011
Traffic Light BehaviorBuild A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …
0 0 1 0 0 1 1 0
0 1 * * 1 0 1 0
1 0 0 1 1 1 0 1
1 1 * * 0 0 0 1
Light
ATraffic Light Behavior
IF A=1
AND B=0
Always
IF A=0
AND B=1
Otherwise
Light BOtherwise
Always
00 01
1011
Traffic Light BehaviorBuild A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …
0 0 1 0 0 1 1 0
0 1 * * 1 0 1 0
1 0 0 1 1 1 0 1
1 1 * * 0 0 0 1
0 0 0 0 0 0 1 0
… … … … … … …
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…
Traffic Light Design
Input: Sensor A
Input: Sensor B
Traffic Light Design
2-bitMemoryRegister
Current State
Write
Sensor A
Sensor B
M1
M2
D1
D2
Traffic Light Design
2-bitMemoryRegisterWrite
Sensor A
Sensor B
Logic For
Next State
&Output 6 Outputs:
for eachLight
Current State
NextState
Traffic Light Design
2-bitMemoryRegisterWrite
Sensor A
Sensor B
Logic For
Next State
&Output 6 Outputs:
for eachLight
Current State
Traffic Light Design
2-bitMemoryRegisterClock
Sensor A
Sensor B
Logic For
Next State
&Output 6 Outputs:
for eachLight
Current State
Design for Any State Machine
MemoryRegisterClock
Inputs
Logic For
Next State
&Output Outputs
Current State
Manybits
State Machinesin Real Life
• Elevator control systems
• Car control systems
• VCR’s
• Alarm Clocks
• Personal Computers
• … Just about everything!
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.)
Light
ATraffic Light Behavior
IF A=1
AND B=0
Always
IF A=0
AND B=1
Otherwise
Light BOtherwise
Always
AlwaysAlways
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!
More Sophisticated Designs• Can also add other State Machines!
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
More Sophisticated Designs
Inputs Outputs
TimerState
Machine
Main StateMachine
Next Time:Computers!
State Machines that you can program
