ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_26.pdf ·...

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ECE 301 – Digital Electronics FSM Design Examples (Lecture #26) The slides included herein were taken from the materials accompanying Fundamentals of Logic Design, 6 th Edition, by Roth and Kinney, and were used with permission from Cengage Learning.

Transcript of ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_26.pdf ·...

ECE 301 – Digital Electronics

FSM Design Examples

(Lecture #26)

The slides included herein were taken from the materials accompanying

Fundamentals of Logic Design, 6th Edition, by Roth and Kinney,

and were used with permission from Cengage Learning.

Spring 2011 ECE 301 - Digital Electronics 2

Sequential Circuit Design1. Understand specifications

2. Draw state graph (to describe state machine behavior)

3. Construct state table (from state graph)

4. Perform state reduction (if necessary)

5. Assign a binary value to each state (state assignment)

6. Create state transition table

7. Select type of Flip-Flop to use

8. Derive Flip-Flop input equations and FSM output equation(s)

9. Draw circuit diagram

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FSM Design

Example #4:

Design a FSM to detect an even number of 1's and an odd number of 0's on an input bit stream (X).

The FSM should output a 1 when the specified conditions are met, and a 0 otherwise.

Requirements:

1. Moore machine2. Gray-code state-assignment3. SR Flip-Flops

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Example #4: State Graph

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Example #4: State Table

Present Next State Output

State X = 0 X = 1 X = 0 X = 1

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Example #4: State Reduction

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Example #4: State Transition Table(using Gray-code state assignment)

A+B+ Z

AB X = 0 X = 1 X = 0 X = 1

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Example #4: SR Excitation Table

Q Q+ S R

0 0 0 x

0 1 1 0

1 0 0 1

1 1 x 0

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Example #4: State Transition Table

A+B+ SARA SBRB

AB X = 0 X = 1 X = 0 X = 1 X = 0 X = 1

(using Gray-code state assignment)

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Example #4: FF Input Equations

SA = RA =

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Example #4: FF Input Equations

SB = RB =

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Example #4: FSM Output Equation

Z =

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Example #4: FSM Circuit Diagram

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FSM Design

Example #5:

Design a FSM to detect an even number of 1's and an odd number of 0's on an input bit stream (X).

The FSM should output a 1 when the specified conditions are met, and a 0 otherwise.

Requirements:

1. Moore machine2. Gray-code state-assignment3. D Flip-Flops

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Example #5: State Transition Table(using Gray-code state assignment)

A+B+ DA DB

AB X = 0 X = 1 X = 0 X = 1 X = 0 X = 1

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Example #5: FF Input Equations

DA = DB =

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Example #5: FSM Output Equation

Z =

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Example #5: FSM Circuit Diagram

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FSM Design

Example #6:

Design a FSM to detect an even number of 1's and an odd number of 0's on an input bit stream (X).

The FSM should output a 1 when the specified conditions are met, and a 0 otherwise.

Requirements:

1. Moore machine2. Gray-code state-assignment3. T Flip-Flops

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Example #6: T Excitation Table

Q Q+ T

0 0 0

0 1 1

1 0 1

1 1 0

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Example #6: State Transition Table(using Gray-code state assignment)

A+B+ TA TB

AB X = 0 X = 1 X = 0 X = 1 X = 0 X = 1

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Questions?