ece 301 – digital electronicsece.gmu.edu/~clorie/spring11/ece-301/lectures/lecture_25.pdfece 301...
TRANSCRIPT
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ECE 301 – Digital Electronics
FSM Design Examples
(Lecture #25)
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.
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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
![Page 3: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/3.jpg)
Spring 2011 ECE 301 - Digital Electronics 3
FSM Design
Example #1:
Design a sequence detector that outputs a 1 when either 011 or 101 is detected.
The FSM does not reset when a sequence is detected.
Requirements:
1. Mealy machine2. Binary state-assignment
![Page 4: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/4.jpg)
Spring 2011 ECE 301 - Digital Electronics 4
Example #1: State Graph
![Page 5: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/5.jpg)
Spring 2011 ECE 301 - Digital Electronics 5
Example #1: State Table
Present Next State Output
State X = 0 X = 1 X = 0 X = 1
![Page 6: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/6.jpg)
Spring 2011 ECE 301 - Digital Electronics 6
Example #1: State Reduction
![Page 7: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/7.jpg)
Spring 2011 ECE 301 - Digital Electronics 7
Example #1: State Transition Table(using Binary state assignment)
A+B+C+ Z
ABC X = 0 X = 1 X = 0 X = 1
![Page 8: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/8.jpg)
Spring 2011 ECE 301 - Digital Electronics 8
FSM Design
Example #2:
Design a sequence detector that outputs a 1 when either 11 or 010 is detected.
The FSM does not reset when a sequence is detected.
Requirements:
1. Mealy machine2. Binary state-assignment3. JK Flip-Flops
![Page 9: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/9.jpg)
Spring 2011 ECE 301 - Digital Electronics 9
Example #2: State Graph
![Page 10: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/10.jpg)
Spring 2011 ECE 301 - Digital Electronics 10
Example #2: State Table
Present Next State Output
State X = 0 X = 1 X = 0 X = 1
![Page 11: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/11.jpg)
Spring 2011 ECE 301 - Digital Electronics 11
Example #2: State Reduction
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Spring 2011 ECE 301 - Digital Electronics 12
Example #2: State Transition Table(using Binary state assignment)
A+B+ Z
AB X = 0 X = 1 X = 0 X = 1
![Page 13: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/13.jpg)
Spring 2011 ECE 301 - Digital Electronics 13
Example #2: JK Excitation Table
Q Q+ J K
0 0 0 x
0 1 1 x
1 0 x 1
1 1 x 0
![Page 14: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/14.jpg)
Spring 2011 ECE 301 - Digital Electronics 14
Example #2: State Transition Table
A+B+ JAKA JBKB
AB X = 0 X = 1 X = 0 X = 1 X = 0 X = 1
(using Binary state assignment)
![Page 15: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/15.jpg)
Spring 2011 ECE 301 - Digital Electronics 15
Example #2: FF Input Equations
JA = KA =
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Spring 2011 ECE 301 - Digital Electronics 16
Example #2: FF Input Equations
JB = KB =
![Page 17: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/17.jpg)
Spring 2011 ECE 301 - Digital Electronics 17
Example #2: FSM Output Equation
Z =
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Spring 2011 ECE 301 - Digital Electronics 18
Example #2: FSM Circuit Diagram
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Spring 2011 ECE 301 - Digital Electronics 19
FSM Design
Example #3:
Design a sequence detector that outputs a 1 when either 11 or 010 is detected.
The FSM does not reset when a sequence is detected.
Requirements:
1. Mealy machine2. Binary state-assignment3. T Flip-Flops
![Page 20: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/20.jpg)
Spring 2011 ECE 301 - Digital Electronics 20
Example #3: T Excitation Table
Q Q+ T
0 0 0
0 1 1
1 0 1
1 1 0
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Spring 2011 ECE 301 - Digital Electronics 21
Example #3: State Transition Table(using Binary state assignment)
A+B+ TA TB
AB X = 0 X = 1 X = 0 X = 1 X = 0 X = 1
![Page 22: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_25.pdfECE 301 – Digital Electronics FSM Design Examples ... Design a sequence detector that outputs](https://reader034.vdocuments.us/reader034/viewer/2022051308/5ae112897f8b9ad47c8b5c21/html5/thumbnails/22.jpg)
Spring 2011 ECE 301 - Digital Electronics 22
Example #3: FF Input Equations
TA = TB =
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Spring 2011 ECE 301 - Digital Electronics 23
Example #3: FSM Output Equation
Z =
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Spring 2011 ECE 301 - Digital Electronics 24
Example #3: FSM Circuit Diagram
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Spring 2011 ECE 301 - Digital Electronics 25
Questions?