Chapter 2 Introduction To Finite State Machines

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Chapter 2Introduction To Finite State Machines

• Presented By Cecilia Parng
• Class C.S. 147
• Prof Sin-Min Lee

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Topics To Cover

• 2.1 State Diagrams And State Tables
• 2.2 Mealy And Moore Machines
• 2.3 Designing State Diagrams

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State Table
Inputs
Present state
Next State
Outputs

• A state table is similar to the truth table
• present state
• all inputs
• next state
• all outputs .

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Important Rule for State Table

• Complete state table must include each possible
  combination of present states and input values,
  and no such combination may match more than one
  row of the table

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State Diagrams

• A state diagram
• Each state is represented by a circled vertex
• Each row of the state table is shown as directed
  arc

J
Y
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Important Rule for State Diagram

• State diagram has same situation as state table.
  Their conditions should be mutually exclusive, no
  input values should meet the condition of more
  than one arc.

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The Alarm Clock
Present state
Turn off alarm
Alarm
Weekday
Next state
On
X
Awake in bed
Yes
Asleep
Awake in bed
Off
Yes
No
Awake and up
No
Awake in bed
Asleep
No
Off
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State Diagram for The Alarm Clock (a)
Alarm
Turn off Alarm Yes
Awake in bed
Asleep
Alarm
Alarm
Alarm /\ Weekday
Alarm /\ Weekday
Awake and up
1 (Always)
( a )
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The alarm clock problem with inaction states
Present state
Alarm
Weekday
Next state
Turn off alarm
Asleep
Asleep
Off
X
No
On
Yes
X
Asleep
Awake in bed
Awake in bed
X
yes
On
Awake in bed
Off
Yes
Awake and up
No
Awake in bed
Awake in bed
Off
No
Asleep
No
X
Awake and up
X
Awake and up
No
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State Diagram for The Alarm Clock (b)
Alarm / 1
Asleep
Awake in bed
Alarm / 0
Alarm / 1
Alarm /\ Weekday / 0
Alarm /\ Weekday / 0
Awake and up
1 (Always) / 0
( b )
1 yes turn off alarm (output) 0 no turn off
alarm (output)
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State Tables for The JK Flip-Flop
Present State
J
K
Next State
Q
Y
0
0
Y
0
Y
0
1
Y
0
Y
1
0
Z
1
Y
1
1
Z
1
Z
0
0
Z
1
Z
0
1
Y
0
Z
1
0
Z
1
Z
1
1
Y
0
( a )
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Condition in Terms of J and K
J
J
K
Z
Y
Q0
Q1
K
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Mealy and Moore Machines

• A finite state machine can represent outputs in
  one of two ways
• Moore Machines
• Mealy Machines

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Moore Machines

• Moore Machines
• Associates its outputs with the states.
• Output values depend only on the state and not on
  the transitions.
• It requires less hardware to produce the output
  values
• It is well suited for representing the control
  units of microprocessors and cpu.

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State Diagram for The Alarm Clock (a)
Alarm
Turn off Alarm Yes
Awake in bed
Asleep
Alarm
Alarm
Alarm /\ Weekday
Alarm /\ Weekday
Awake and up
1 (Always)
Moore Machine
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Mealy Machines

• Mealy Machines
• Associates outputs with the transitions.
• It depends on both its state and its input values

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State Diagram for The Alarm Clock (b)
Alarm / 1
Asleep
Awake in bed
Alarm / 0
Alarm / 1
Alarm /\ Weekday / 0
Alarm /\ Weekday / 0
Awake and up
1 (Always) / 0
Mealy Machine
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Designing State Diagrams

• Counter
• String Checker
• Toll Booth

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Modulo 6 Counter

• A modulo 6 counter is a 3-bit counter that counts
  through the sequence.
• 000 001 010 011 100 101 000
• 0 1 2 3 4 5 0
• Unlike a regular 3-bit counter
• 110(6) and 111(7) do not count

0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
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State Table for The Modulo 6 Counter
Present State
Next State
C
V2 V1 V0
U
S0
0
S0
1
0 0 0
S0
1
S1
0
0 0 1
S1
0
S1
0
0 0 1

S1
1

S2
0
0 1 0
S2
0
S2
0
0 1 0
S2
1
S3
0
0 1 1
S3
0
S3
0
0 1 1
S3
0

1 0 0
1
S4
S4
0
S4
0
1 0 0
S4
1
S5
0
1 0 1
S5
0
S5
0
1 0 1
S5
1
S0
1
0 0 0
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State Diagram for The Modulo 6 Counter (Mealy)
0 / 1000
0 / 0001
0 / 0010
S0
S1
S2
1 / 0001
1 / 0010
1 / 1000
1 / 0011
S5
S4
S3
1 / 0101
1 / 0100
0 / 0101
0 / 0011
0 / 0100
( a ) Mealy
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State Diagram for The Modulo 6 Counter (Moore)
C0 V0010
C1 V 000
C0 V010
S0
S1
U
U
S2
U
U
U
U
U
S5
S4
S3
U
U
U
U
C0 V011
C0 V100
C0 V101
( b ) Moore
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String Checker

• A String Checker inputs a string of
• bits, one bits per clock cycle.
• It checks bits 1,2, and 2, then 2,3,and 4 and so
  forever

0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
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State Table For String Checker
Present State
L
Next State
M
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
S0 S1 S2 S3 S4 S5 S6 S7 S0 S1 S2 S3 S4 S5 S6 S7
0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0
S0 S0 S1 S1 S2 S2 S3 S3 S4 S4 S5 S5 S6 S6 S7 S7
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State Diagrams for the String Checker ( Mealy)
0/0
S5
S4
S6
1/0
0/0
0/1
0/1
0/0
1/0
S7
0/1
S0
1/0
0/0
1/0
0/0
1/0
1/0
S3
S1
S2
0/0
1/0
Mealy
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State Diagrams for the String Checker (Moore)
I
M0
M1
M0
I
S6
S5
S4
I
I
I
I
S7
I
S0
I
I
I
I
I
M0
M0
I
I
S3
S2
S1
I
M0
M0
M0
I
Moore
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Toll Booth Controller

• A toll booth controller has two external sensors.
• Indicates a car is at the toll booth
• Indicates a coin has been deposited in the toll
  booths collection basket and its value

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States for the toll booth controller
State
Condition
R G A
SNOCAR S0 S5 S10 S15 S20 S25 S30 Spaid Scheat
No car in toll booth

1 0 0
Car in toll booth, 0 cents paid
1 0 0
Car in toll booth, 5 cents paid
1 0 0
Car in toll booth, 10 cents paid
1 0 0
Car in toll booth, 15 cents paid
1 0 0
Car in toll booth, 20 cents paid
1 0 0
Car in toll booth, 25 cents paid
1 0 0
Car in toll booth, 30 cents paid
1 0 0
Car in toll booth, full toll paid
0 1 0
Car left toll booth without paying full toll
1 0 1
I1I0 00 no coin has been deposited I1I0
01 nickel has been deposited I1I0 10 dime has
been deposited I1I0 11 quarter has been
deposited
R Red light G Green light A Alarm C 1 Car
enters the toll booth C 0 No car arrives
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The End

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