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CS 3410 Computer Science Cornell University The slides are the product of many rounds of teaching CS 3410 by Professors Weatherspoon Bala Bracy and Sirer Goals for Today Finite ID: 720078 Download Presentation

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output state outputs input state output input outputs logic machine diagram fsm states door lock inputs current moore finite

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## Presentation on theme: "Finite State Machines Hakim Weatherspoon"— Presentation transcript

Slide1

Finite State Machines

Hakim WeatherspoonCS 3410Computer ScienceCornell University

The slides are the product of many rounds of teaching CS

3410

by Professors

Weatherspoon,

Bala

,

Bracy

,

and

Sirer

.Slide2

Goals for Today

Finite State Machines (FSM)How do we design logic circuits with state?

Types of FSMs: Mealy and Moore Machines

Examples: Serial Adder and a Digital Door LockSlide3

Finite State MachinesSlide4

Next Goal

How do we design logic circuits with state?Slide5

Finite State Machines

An electronic machine which hasexternal inputsexternally visible outputsinternal stateOutput and next state depend oninputs

current stateSlide6

Abstract Model of FSM

Machine is M = ( S, I, O,

)

S

: Finite set of states

I

:

Finite

set of inputs

O

: Finite set of outputs

:

State

transition

function

Next state

depends on

present input

and

present stateSlide7

Automata Model

Finite State Machine

inputs from external world

outputs to external world

internal state

combinational logic

Next

State

Current State

Input

Output

Registers

Comb.

LogicSlide8

FSM Example

Legend

state

input

/

output

start

state

A

B

C

D

down

/

on

up

/

off

down

/

on

down

/

off

up

/

off

down

/

off

up

/

off

up

/

off

Input:

up

or

down

Output:

on

or

off

States:

A

,

B

,

C

, or

DSlide9

FSM Example

Legend

state

input

/

output

start

state

A

B

C

D

down

/

on

up

/

off

down

/

on

down

/

off

up

/

off

down

/

off

up

/

off

up

/

off

Input: =

up

or =

down

Output: =

on

or =

off

States: =

A

, =

B

, =

C

, or =

DSlide10

FSM Example

Legend

S

1

S

0

i

0

i

1

i

2

/

o

0

o

1

o

2

S

1

S

0

00

01

10

11

1

/

1

0

/

0

1

/

1

1

/

0

0

/

0

1

/

0

0

/

0

0

/

0

Input:

0

=up or

1

=down

Output:

1

=on or

0

=off

States:

00

=A,

01

=B,

10

=C, or

11

=DSlide11

General Case:

Mealy Machine

Outputs and next state depend on both

current state and input

Mealy Machine

Next State

Current State

Input

Output

Registers

Comb.

LogicSlide12

Moore Machine

Special Case: Moore Machine

Outputs depend only on current state

Next

State

Current State

Input

Output

Registers

Comb.

Logic

Comb.

LogicSlide13

Moore Machine FSM Example

Legend

state

out

input

start

out

A

off

B

on

C

off

D

off

down

up

down

down

up

up

down

up

Input:

up

or

down

Output:

on

or

off

States:

A

,

B

,

C

, or

DSlide14

Mealy Machine FSM Example

Legend

state

input

/

output

start

state

A

B

C

D

down

/

on

up

/

off

down

/

on

down

/

off

up

/

off

up

/

off

down

/

off

up

/

off

Input:

up

or

down

Output:

on

or

off

States:

A

,

B

,

C

, or

DSlide15

Activity#2: Create a Logic Circuit for a Serial

lsb

)

first

How many states are needed to represent FSM?

Draw and Fill in FSM diagram

10110

…01111

…00101

Strategy

:

(1) Draw a state diagram (e.g. Mealy Machine)

(2) Write output and next-state tables

(3) Encode states, inputs, and outputs as bits

(4) Determine logic equations for next state and outputs

Sum: outputSlide16

FSM: State Diagram

states

:

Inputs

:

???

and

???

Output

:

???

.

…10110

…01111

…00101Slide17

FSM: State Diagram

S0

S1

__

/

_

__

/

_

__

/

_

__

/

_

__

/

_

__

/

_

__

/

_

__

/

_

10110

…01111

…00101

states

:

Inputs

:

???

and

???

Output

:

???

.Slide18

FSM: State Diagram

??

??

Current state

?

Next state

(2) Write down all input and state combinations

S0

S1

__

/

_

__

/

_

__

/

_

__

/

_

__

/

_

__

/

_

__

/

_

__

/

_Slide19

FSM: State Diagram

??

??

Current state

?

Next state

(3) Encode states, inputs, and outputs as bits

S0

S1

__

/

_

__

/

_

__

/

_

__

/

_

__

/

_

__

/

_

__

/

_

__

/

_Slide20

FSM: State Diagram

??

??

Current state

?

Next state

(4) Determine logic equations for next state and outputsSlide21

Example: Digital Door Lock

Digital Door LockInputs:

keycodes

clock

Outputs:

“unlock” signal

display how many keys pressed so farSlide22

Door Lock: Inputs

Assumptions:signals are synchronized to clockPassword is B-A-B

K

A

B

K

A

B

Meaning

0

0

0

Ø

(

no key)

1

1

0

‘A’ pressed

1

0

1

‘B’ pressedSlide23

Door Lock: Outputs

Assumptions:High pulse on U unlocks door

U

D

3

D

2

D

1

D

0

4

LED

dec

8

Strategy

:

(1) Draw a state diagram (e.g. Moore Machine)

(2) Write output and next-state tables

(3) Encode states, inputs, and outputs as bits

(4) Determine logic equations for next state and outputsSlide24

Door Lock: Simplified State Diagram

(1) Draw a state diagram (e.g. Moore Machine)Slide25

Door Lock: Simplified State Diagram

any

Cur.

State

Output

(

2) Write output and next-state

tables Slide26

Door Lock: Simplified State Diagram

G2

G3

”2”

”3”, U

Ø

“B”

any

else

Cur. State

Input

Next State

Cur. State

Input

Next State

(

2) Write output and next-state

tables Slide27

Door Lock: Implementation

4

dec

3bit

Reg

clk

U

D

3-0

S

2-0

S’

2-0

S

2-0

K

A

B

D

3

D

2

D

1

D

0

U

S

2

S

1

S

0

(4) Determine logic equations for next state and outputsSlide28

Door Lock: Implementation

4

dec

3bit

Reg

clk

U

D

3-0

S

2-0

S’

2-0

S

2-0

K

A

B

S

2

S

1

S

0

S’

2

S’

1

S’

0

K

A

B

(4) Determine logic equations for next state and outputsSlide29

Door Lock: Implementation

4

dec

3bit

Reg

clk

U

D

3-0

S

2-0

S’

2-0

S

2-0

K

A

B

Strategy

:

(1) Draw a state diagram (e.g. Moore Machine)

(2) Write output and next-state tables

(3) Encode states, inputs, and outputs as bits

(4) Determine logic equations for next state and outputsSlide30

Door Lock: Implementation

Strategy

:

(1) Draw a state diagram (e.g. Moore Machine)

(2) Write output and next-state tables

(3) Encode states, inputs, and outputs as bits

(4) Determine logic equations for next state and outputs

Next

State

Current State

Input

Output

Registers

Comb.

Logic

Comb.

Logic

Moore MachineSlide31

Goals for today

ReviewFinite State MachinesSlide32

Summary

We can now build interesting devices with sensorsUsing combinational logicWe can also store data values

Stateful circuit elements (D Flip Flops, Registers, …)

State