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Chapter 2Chapter 2Introduction To Finite State Introduction To Finite State

MachinesMachines

Chapter 2Chapter 2Introduction To Finite State Introduction To Finite State

MachinesMachines

Presented By: Cecilia Parng

Class: C.S. 147

Prof: Sin-Min Lee

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Topics To CoverTopics 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 TableState TableState TableState Table

Present state

Inputs Next State Outputs

A state table is similar to the truth tablepresent stateall inputsnext 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 DiagramsState 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 The Alarm Clock

Present state Alarm Weekday Next state Turn off alarm

On X Awake in bed YesAsleep

Awake in bed Off Yes Awake and up No

Awake in bed Off No Asleep No

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State Diagram for The Alarm Clock State Diagram for The Alarm Clock (a)(a)

Awake in bedAsleepAlarm’ Alarm

Awake and up

1 (Always)

Alarm

Alarm’ /\ Weekday’ Alarm’ /\ Weekday

Turn off Alarm = Yes

( a )

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The alarm clock problem with The alarm clock problem with inactioninaction statesstates

Present state Alarm Weekday Next state Turn off alarm

Asleep Off X Asleep No

Asleep On Awake in bed Yes

Awake in bed On X Awake in bed yes

Awake in bed Off Yes Awake and up No

Awake in bed Off No Asleep No

Awake and up X X Awake and up No

X

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State Diagram for The Alarm ClockState Diagram for The Alarm Clock (b)

( b )

Asleep Awake in bed

Awake and up

Alarm’ / 0

Alarm / 1

Alarm’ /\ Weekday’ / 0

1 (Always) / 0

Alarm’ /\ Weekday / 0

Alarm / 1

1 = yes turn off alarm (output)

0 – no turn off alarm (output)

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State Tables for The JK Flip-FlopState Tables for The JK Flip-Flop

( a )

Present State

Y

Z

Z

Z

Z

Y

Y

Y

J K

0

0

1

1

0

0

1

1

0

1

0

1

0

1

0

1

Next State Q

Y

Y

Z

Z

Z

Y

Z

Y

0

0

1

1

1

0

1

0

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Condition in Terms of J and KCondition in Terms of J and K

Z

J

K

J’ K’

Q=0 Q=1

Y

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Mealy and Moore MachinesMealy and Moore Machines

A finite state machine can represent outputs in one of two ways

Moore Machines

Mealy Machines

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Moore MachinesMoore 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 State Diagram for The Alarm Clock (a)(a)

Awake in bedAsleepAlarm’ Alarm

Awake and up

1 (Always)

Alarm

Alarm’ /\ Weekday’ Alarm’ /\ Weekday

Turn off Alarm = Yes

Moore Machine

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Mealy MachinesMealy 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 ClockState Diagram for The Alarm Clock (b)

Mealy Machine

Asleep Awake in bed

Awake and up

Alarm’ / 0

Alarm / 1

Alarm’ /\ Weekday’ / 0

1 (Always) / 0

Alarm’ /\ Weekday / 0

Alarm / 1

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Designing State DiagramsDesigning State Diagrams

Counter

String Checker

Toll Booth

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Modulo 6 CounterModulo 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 CounterState Table for The Modulo 6 CounterPresent State Next State C V2 V1 V0U

S0

S0

S1

S1

S2

S2

S3

S3

S4

S4

S5

S5

1

0

0

1

0

1

0

1

0

1

0

1

S0

S1

S1

S2

S2

S3

S3

S4

S4

S5

S5

S0

1

0

0

0

0

0

0

0

0

0

0

1

0 0 0

0 0 1

0 0 1

0 1 0

0 1 0

0 1 1

0 1 1

1 0 0

1 0 1

1 0 1

0 0 0

1 0 0

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State Diagram for The Modulo 6 State Diagram for The Modulo 6 Counter (Mealy)Counter (Mealy)

S0

S5

S1

S4

S2

S3

0 / 1000 0 / 0001 0 / 0010

1 / 0001 1 / 0010

1 / 0011

0 / 0011

1 / 0100

0 / 0100

1 / 0101

0 / 0101

1 / 1000

( a ) Mealy

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State Diagram for The Modulo 6 State Diagram for The Modulo 6 Counter (Moore)Counter (Moore)

S5

S0 S1

S4

S2

S3

U’

U’

U’

U’

U’

U’

C=1

V =000

U

C=0

V=0010

U

C=0

V=010

U

C=0

V=011

U

C=0

V=100

U

C=0

V=101

( b ) Moore

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String CheckerString 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 CheckerState Table For String CheckerPresent State

S0

S0

S1S1

S2

S2

S3

S3

S4

S4

S5

S5

S6

S6

S7

S7

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

L Next State

S0

S1

S2

S3

S4

S5

S6

S7

S0

S1

S2

S3

S4

S5

S6

S7

M

0

0

0

0

0

0

1

0

0

0

0

0

0

0

1

0

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State Diagrams for the String Checker State Diagrams for the String Checker ( Mealy)( Mealy)

S3

S7 S0

S1

S4S6S5

S2

0/0

0/0

0/01/0

1/00/0

0/0

0/01/0

1/0

0/10/1

0/1

1/01/0

1/0

Mealy

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State Diagrams for the String State Diagrams for the String Checker (Moore)Checker (Moore)

S7 S0

S6 S5 S4

S3 S2 S1

M=1

I’M=0

I’

I’

M=0I

M=0

IM=0

I

M=0

I

I’

I’

I

I I I’I’ I

I’M=0

M=0

Moore

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Toll Booth ControllerToll 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 booth’s collection basket and its value

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States for the toll booth controllerStates for the toll booth controller

State Condition

SNOCAR

S0

S5

S10

S15

S20

S25

S30

Spaid

Scheat

No car in toll booth

Car in toll booth, 0 cents paid

Car in toll booth, 5 cents paid

Car in toll booth, 10 cents paid

Car in toll booth, 15 cents paid

Car in toll booth, 20 cents paid

Car in toll booth, 25 cents paid

Car in toll booth, 30 cents paid

Car in toll booth, full toll paid

Car left toll booth without paying full toll

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

1 0 0

0 1 0

1 0 1

R G A

R Red light

G Green light

A Alarm

C = 1 Car enters the toll booth

C = 0 No car arrives

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

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The EndThe End

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