Traffic Light Behavior

1
Traffic Light Behavior
IF A1 AND B0
2
Traffic Light Behavior
Otherwise
IF A1 AND B0
3
Traffic Light Behavior
Otherwise
IF A1 AND B0
Always
4
Traffic Light Behavior
Otherwise
IF A1 AND B0
Always
IF A0 AND B1
Otherwise
5
Traffic Light Behavior
Otherwise
IF A1 AND B0
Always
Always
IF A0 AND B1
Otherwise
6
Traffic Light Behavior
Otherwise
NoteClock beats every 4 sec.So Light is
Yellow for 4 sec.
IF A1 AND B0
Always
Always
IF A0 AND B1
Otherwise
7
Traffic Light State Machine
Otherwise
NoteClock beats every 4 sec.So Light is
Yellow for 4 sec.
IF A1 AND B0
Always
Always
IF A0 AND B1
Otherwise
8
Traffic Light Design

• Weve 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?

9
Traffic Light Design

• Thinking this through
• Our machine needs to

10
Traffic Light Design

• Thinking this through
• Our machine needs to
• Remember which state it is in (Memory)

11
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)

12
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 thats all !

13
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!

14
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.

15
Traffic Light States
Otherwise
IF A1 AND B0
Light A
Always
Always
IF A0 AND B1
Otherwise
Light B
16
Traffic Light States
Otherwise
IF A1 AND B0
01
00
Light A
Always
Always
IF A0 AND B1
11
10
Otherwise
Light B
17
Traffic Light Design

• Problem 2
• Given the state it is in and input values, it
  must determine which state to go tonext (Logic)
• Answer

18
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!

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Traffic Light Behavior
Build A Truth Table for next state / Output
20
Traffic Light Behavior
Otherwise
IF A1 AND B0
01
00
Light A
Always
Always
IF A0 AND B1
11
10
Otherwise
Light B
21
Traffic Light Behavior
Build A Truth Table for next state / Output
22
Traffic Light Behavior
Otherwise
IF A1 AND B0
01
00
Light A
Always
Always
IF A0 AND B1
11
10
Otherwise
Light B
23
Traffic Light Behavior
Build A Truth Table for next state / Output
24
Traffic Light Behavior
Otherwise
IF A1 AND B0
01
00
Light A
Always
Always
IF A0 AND B1
11
10
Otherwise
Light B
25
Traffic Light Behavior
Build A Truth Table for next state / Output
26
Traffic Light Behavior
Otherwise
IF A1 AND B0
01
00
Light A
Always
Always
IF A0 AND B1
11
10
Otherwise
Light B
27
Traffic Light Behavior
Build A Truth Table for next state / Output
28
Traffic Light Behavior
Otherwise
IF A1 AND B0
01
00
Light A
Always
Always
IF A0 AND B1
11
10
Otherwise
Light B
29
Traffic Light Behavior
Build A Truth Table for next state / Output
30
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)
• Lets put it together

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Traffic Light Design
Input Sensor A
Input Sensor B
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Traffic Light Design
Current State
D1
M1
2-bit Memory Register
D2
M2
Write
Sensor A
Sensor B
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Traffic Light Design
Current State
Next State
2-bit Memory Register
Logic For Next State Output
Write
Sensor A
6 Outputs for eachLight
Sensor B
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Traffic Light Design
Current State
2-bit Memory Register
Logic For Next State Output
Write
Sensor A
6 Outputs for eachLight
Sensor B
35
Traffic Light Design
Current State
2-bit Memory Register
Logic For Next State Output
Clock
Sensor A
6 Outputs for eachLight
Sensor B
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Design for Any State Machine
Manybits
Current State
Memory Register
Logic For Next State Output
Clock
Inputs
Outputs
37
State Machinesin Real Life

• Elevator control systems
• Car control systems
• VCRs
• Alarm Clocks
• Personal Computers
• Just about everything!

38
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.)

39
Traffic Light Behavior
Otherwise
IF A1 AND B0
Always
Always
Light A
Always
Always
IF A0 AND B1
Otherwise
Light B
40
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!

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More Sophisticated Designs

• Can also add other State Machines!

42
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

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More Sophisticated Designs
Inputs
Outputs
Timer StateMachine
44
Computers!
State Machines that you can program
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Review

• In designing state machines, we used
• Binary Representation (to represent states)
• Memory (to store the current state)
• Logic Circuits Universal Method (to determine
  the next state)
• In this way, we learned how to buildspecial-purpo
  se digital systems(e.g. traffic lights)

46
General Purpose Computers

• What makes a PC different?
• Today your PC cant play Final Fantasy X.
• Tonight, you buy the Final Fantasy X CD-ROM
• Tomorrow your PC can play the game!
• PCs are general-purpose computers.
• Realize state machines for traffic lights,
  digital cameras, VCRs,
• You can write a program (software) to control the
  circuitry (hardware) of a general purpose computer

47
The Stored Program

• Idea is simple
• Build a machine that can execute certain
  instructions.
• Then, write down different lists of instructions
  (programs) to accomplish different things.
• One program plays an adventure game
• Another program lets you write papers
• Another lets you surf the Web

48
Programming

• Using software to control hardware
• Hardware is fixed circuitry
• Software is instructions to the processor to
  control the inputs to the fixed circuitry
• Inputs to the hardware are of 2 types
• Data
• Program
• We dont differentiate
• Both are stored in computers memory

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History of ProgrammableMachines

• First programmablesystem was the early
  printing process developed in China circa 800
  C.E.
• First program wasperhaps Chinese translation
  ofBuddhist Canon(the Tipitaka)

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History (cont.)

• Gutenbergs Printing Press(circa 1450)
• Main Contribution
• Just a few basic instructions
  (smalleralphabet size) suffice.

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History (cont.)

• Huygens Pendulum Clock(circa 1650)
• Main Contribution
• Timing, clock ticks increase accuracy

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History (cont.)

• Musical Machines Barrel Organs (1500!) Music
  boxes (between) Player Pianos (c. 1700)
• Main Contributions
• Drive cylinder or disk with pins (bits!!) which
  play notes at the right time
• Change disk -gt change song!!

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History (cont.)

• Jacquards Loom(circa 1810)

• Punched Cards stored program for
  weaving patterns.

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History (cont.)
                                             

• Charles Babbage (1822-64)
• Input -- Punched Cards
• Hardware -- general-purpose
  mechanical mathematical system
• (Analytical Engine) -- never built
• Could be programmed
• punched card could sayGo back 5 punched cards
• Instructions could be Executed repeatedly, or in
  different order.

55
The Modern Computer
von Neumann (1945) Princeton, NJ

• Basic Idea still the sameA machine that can
  execute certain instructions.
• Machine instructions represented by sequences of
  0s and 1s(Machine Language)
• Instructions, and data, stored in Memory

56
Memory

• Weve seen that memory can be used to build State
  Machines.
• In modern computers, memory is also usedin a
  different way
• Big arrays of Memory called RAM Random Access
  Memory
• RAM is a place to store information while the
  computer is running
• The information includes the data that the
  program reads and writes, as well as the program
  itself (I.e. its instructions)

57
Programs are Just Like Data

• One of the important features of the von Neumann
  model is the fact that
• The instructions themselves
• And
• The data the instructions manipulate
• are all stored in the same RAM.
• This was one of the revolutionary features of the
  modern computer, totally unlike Punch-Card
  computers proposed in the past.

58
Programs are Just Like Data

• This innovation is crucial to modern computing.
• It even allows for the possibility of programs
  that change themselves as they are executed.
• With great power comes great risk
• Computer Viruses!

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How Memory (RAM) Works

• Take a single bit of memory

D
M
Write
60
RAM (cont.)

• Group 8 of them together.
• 8 bits (b)is called abyte (B).
• Most RAMis arrangedin bytes.

61
RAM (cont.)

• A byte of memory (a.k.a. an 8-bit register)

8 bits input
8 bits Output
8 bits (1 byte)of Memory
Write
62
RAM (cont.)

• We want a HUGE number of such 1 byte memory
  cells.

63
RAM (cont.)

• We want a HUGE number of such 1 byte memory
  cells.
• Problem How do we indicate which byte ofmemory
  we want to use at any given time?

64
RAM (cont.)

• Solution Assign each byte an address.
• We can number all the bytes in binary.
• Each bytes assigned number is called the bytes
  address in memory.
• Then, we can ask the RAM
• What is byte number 011010101010?
• Or tell the RAM
• Write 01101100 into memory at
  address011010101010

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RAM (cont.)
Address
Data Output
Data input
Write
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RAM (cont.)
20 bits of address
Address
Data Output
Data input
Write
67
RAM (cont.)
20 bits of address
Address
Data Output
Data input
Write
8 bits (1 byte)of data