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Finite-State Machine

Muhammad Irfan Anjum

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OUTLINE

• Introduction

• Types of Finite State Machines

• Mealy State Machine

• Moore State Machine

• Example

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• FSMs are different from counters in the sense that they

have external I/Ps, and state transitions are dependent on

these I/Ps and the current state.

• Simple forms of pattern matching.

• Models for sequential logic circuits, of the kind on which

every present-day computer and many device controllers is

based.

Finite State Machine

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FFs

External I/Ps External O/Ps

m1 m2

nn

Comb.Logic

CLK

FFsn

CLK

n

OutputLogic

m2

Next StateComb.Logic

m1

ExternalI/Ps

External Outputs

Mealy Machine Model Moore Machine Model

even odd

Mealy and Moore Machines

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Difference Between Mealy and Moore Machine

Mealy Moore (1) O/Ps depend on the present O/Ps depend only on the state and present I/Ps present state(2) The O/P change asyn Since the O/Ps change -chronously with the when the state changes, enabling clock edge and the state change is synchronous with the enabling clock edge, O/Ps change synchronously with this clock edge(3) A counter is not a Mealy A counter is a Moore machine machine(4) A Mealy machine will have the same # or fewer states than a Moore machine

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Finite State Machine (FSM) Design

Example:There is a one bit-serial I/P line. Design an FSM that outputs a ‘0’ if an even # of 1’s have been received on the I/P line and the outputs a ‘1’ otherwise.

FSMx O/p y

CLK

CLK

x

# of1s

even(0)

odd(1)

even(2)

odd(3)

odd(3)

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Solution 1: (Mealy)0/0

Even

Odd

1/11/0

0/1

Reset0

Even

11

0

Reset[0]

Odd [1]

Output

InputOutput

Input

Transition Arc

Output is dependent only on current state

O/P is dependenton current state andinput in Mealy

Solution 2: (Moore)

Mealy Machine: Output is associatedwith the state transition, and appearsbefore the state transition is completed(by the next clock pulse).

Moore Machine: Output is associatedwith the state and hence appearsafter the state transition take place.

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State Transition Table

(Even-Parity Checker)

Even State: 0 ; Odd State: 1; State Variable A

A x A+ y1 y2 DA

0 0 0 0 0 0

0 1 1 0 1 1

1 0 1 1 1 1

1 1 0 1 0 0

PresentState

InputNextState

MooreO/P

MealyO/P

D-FFExcit.

Input variablesto comb. logic

QFF

N.S. & O/PLogic

CLK

x y2

A DA

Or

FFs

y1

N.S.Logic

O/PLogic

DAAQ

x

DA= Ax ; y1 = A for Moorey2 = Ax for Mealy

Output functions

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Moore M/C Implementation

D Q

QRCLK

y1x=1

A0

a) D-FF

Moore O/P is synchronized with clock.

Mealy M/C Implementation

D Q

QRCLK

y2

x=1A

0 1

a) D-FF

Mealy O/P is not synchronized with clock.

Reset

Reset