ece 301 – digital electronicsece.gmu.edu/~clorie/spring11/ece-301/lectures/lecture_20.pdfspring...
TRANSCRIPT
![Page 1: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/1.jpg)
ECE 301 – Digital Electronics
Counters
(Lecture #20)
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.
![Page 2: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/2.jpg)
Spring 2011 ECE 301 - Digital Electronics 2
Counters
● A counter is a sequential circuit (aka. finite state machine) that cycles through a fixed sequence of states.
● The state of the counter is stored in Flip-Flops.
● An n-bit counter
– has n Flip-Flops
– can cycle through at most 2n states.
![Page 3: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/3.jpg)
Spring 2011 ECE 301 - Digital Electronics 3
Counters
00
10
0111010110
000 001111
011100101
2-bit Counter
3-bit Counter
![Page 4: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/4.jpg)
Spring 2011 ECE 301 - Digital Electronics 4
Counters
2-bit Counter
3-bit Counter
00
01
10
using only 3 states
using only 5 states
010
101 011
000
110
![Page 5: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/5.jpg)
Spring 2011 ECE 301 - Digital Electronics 5
Binary Counters
● An n-bit binary counter is a counter that cycles through all 2n states in ascending (or descending) order.
010110
000 001111
011100101
3-bit Binary Counter
Cycles through all 8 states
in ascending order
![Page 6: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/6.jpg)
Spring 2011 ECE 301 - Digital Electronics 6
Binary Counters: Design
1.Draw a state graph that specifies the desired sequence of the counter.
2.Construct a state table from the state graph.
One Flip-Flop for each bit in the state.
3.Derive a K-map from the state table for each Flip-Flop input.
Select the type of Flip-Flop to be used.
4.Determine the input equation(s) for each Flip-Flop.
![Page 7: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/7.jpg)
Spring 2011 ECE 301 - Digital Electronics 7
Binary Counters: Design
Example: State Table (using D FF)
Present State Next State FF Inputs
C B A C+ B+ A+ DC DB DA
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 0 1 0 1
1 0 1 1 1 0
1 1 0 1 1 1
1 1 1 0 0 0
Q+ = D
CharacteristicEquation:
![Page 8: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/8.jpg)
Spring 2011 ECE 301 - Digital Electronics 8
Binary Counters: Design
Example: K-maps (for D FF inputs)
![Page 9: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/9.jpg)
Spring 2011 ECE 301 - Digital Electronics 9
Binary Counters: Design
Example: Circuit Diagram (using D FF)
![Page 10: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/10.jpg)
Spring 2011 ECE 301 - Digital Electronics 10
Binary Counters: Design
Example: State Table (using T FF)
Q+ = T xor Q
CharacteristicEquation:
Present State Next State FF Inputs
C B A C+ B+ A+ TC TB TA
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 0 1 0 1
1 0 1 1 1 0
1 1 0 1 1 1
1 1 1 0 0 0
Excitation Table:
Q Q+ T
0 0 0
0 1 1
1 0 1
1 1 0
![Page 11: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/11.jpg)
Spring 2011 ECE 301 - Digital Electronics 11
Binary Counters: Design
Example: K-maps (for T FF inputs)
![Page 12: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/12.jpg)
Spring 2011 ECE 301 - Digital Electronics 12
Binary Counters: Design
Example: Circuit Diagram (using T FF)
![Page 13: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/13.jpg)
Spring 2011 ECE 301 - Digital Electronics 13
Binary Up-Down Counters
What constraints must be placed on the U and D control signals?
![Page 14: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/14.jpg)
Spring 2011 ECE 301 - Digital Electronics 14
Binary Up-Down Counters
![Page 15: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/15.jpg)
Spring 2011 ECE 301 - Digital Electronics 15
Loadable Counter with Enable
![Page 16: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/16.jpg)
Spring 2011 ECE 301 - Digital Electronics 16
Counters: Design
1.Draw a state graph that specifies the desired sequence of the counter.
2.Construct a state table from the state graph.
One Flip-Flop for each bit in the state.
3.Derive a K-map from the state table for each Flip-Flop input.
Select the type of Flip-Flop to be used.
4.Determine the input equation(s) for each Flip-Flop.
![Page 17: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/17.jpg)
Spring 2011 ECE 301 - Digital Electronics 17
Counters: Design
Example:
Design the following counter using D Flip-Flops.
![Page 18: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/18.jpg)
Spring 2011 ECE 301 - Digital Electronics 18
Counters: Design
Example: State Table (using D FF)
Present State Next State FF Inputs
C B A C+ B+ A+ DC DB DA
0 0 0 1 0 0
0 0 1 x x x
0 1 0 0 1 1
0 1 1 0 0 0
1 0 0 1 1 1
1 0 1 x x x
1 1 0 x x x
1 1 1 0 1 0D = Q+
ExcitationEquation:
![Page 19: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/19.jpg)
Spring 2011 ECE 301 - Digital Electronics 19
Counters: Design
Example: K-maps (for D FF inputs)
DC DB DA
![Page 20: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/20.jpg)
Spring 2011 ECE 301 - Digital Electronics 20
Counters: Design
Example: Circuit Diagram (using D FF)
![Page 21: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/21.jpg)
Spring 2011 ECE 301 - Digital Electronics 21
Counters: Design
Example:
Design the following counter using T Flip-Flops.
![Page 22: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/22.jpg)
Spring 2011 ECE 301 - Digital Electronics 22
Counters: Design
Example: State Table (using T FF)
Present State Next State FF Inputs
C B A C+ B+ A+ TC TB TA
0 0 0 1 0 0
0 0 1 x x x
0 1 0 0 1 1
0 1 1 0 0 0
1 0 0 1 1 1
1 0 1 x x x
1 1 0 x x x
1 1 1 0 1 0T = Q xor Q+
ExcitationEquation:
![Page 23: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/23.jpg)
Spring 2011 ECE 301 - Digital Electronics 23
Counters: Design
Example: K-maps (for T FF inputs)
![Page 24: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/24.jpg)
Spring 2011 ECE 301 - Digital Electronics 24
Counters: Design
Example: K-maps (for T FF inputs)
We could derive TC , TB , and TA directly from the state table,
but it is often more convenient to plot next-state maps
showing C+, B+, and A+ as functions of C, B, and A, and then
derive TC , TB , and TA from these maps.
![Page 25: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/25.jpg)
Spring 2011 ECE 301 - Digital Electronics 25
Counters: Design
Example: Circuit Diagram (using T FF)
![Page 26: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/26.jpg)
Spring 2011 26
Counters: Design
Example: Next States (for T FF inputs)
Although the original state table for the counter is not
completely specified, the next states of states 001, 101,
and 110 have been specified in the process of
completing the circuit design
110101
![Page 27: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/27.jpg)
Spring 2011 ECE 301 - Digital Electronics 27
Counters: Design
Example:
Design the following counter using JK Flip-Flops.
![Page 28: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/28.jpg)
Spring 2011 ECE 301 - Digital Electronics 28
Counters: Design
Example: Using JK Flip-Flops
Excitation Table:
Q Q+ J K
0 0 0 x
0 1 1 x
1 0 x 1
1 1 x 0
![Page 29: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/29.jpg)
Spring 2011 ECE 301 - Digital Electronics 29
Counters: Design
Example: State Table (using JK FF)
Present State Next State FF Inputs
C B A C+ B+ A+ JC KC JB KB JA KA
0 0 0 1 0 0
0 0 1 x x x
0 1 0 0 1 1
0 1 1 0 0 0
1 0 0 1 1 1
1 0 1 x x x
1 1 0 x x x
1 1 1 0 1 0
![Page 30: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/30.jpg)
Spring 2011 ECE 301 - Digital Electronics 30
Counters: Design
Example: K-maps (for JK FF inputs)
![Page 31: ECE 301 – Digital Electronicsece.gmu.edu/~clorie/Spring11/ECE-301/Lectures/Lecture_20.pdfSpring 2011 ECE 301 - Digital Electronics 6 Binary Counters: Design 1. Draw a state graph](https://reader033.vdocuments.us/reader033/viewer/2022051508/5aa193c27f8b9a80378bd4df/html5/thumbnails/31.jpg)
Spring 2011 ECE 301 - Digital Electronics 31
Counters: Design
Example: Circuit Diagram (using JK FF)
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Spring 2011 ECE 301 - Digital Electronics 32
Questions?