Digital Systems I

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# Digital Systems I - PowerPoint PPT Presentation

Digital Systems I. EEC 180A Lecture 15 Bevan M. Baas Tuesday, November 20, 2007. Counter Example. 3-bit counter Specification Starting at zero, it increments by 3 at 6, it wraps back to 0 Has a reset signal input When reset =1, the next counter value is 0 Uses D Flip-flops. reset.

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### Digital Systems I

EEC 180A

Lecture 15

Bevan M. Baas

Tuesday, November 20, 2007

Counter Example
• 3-bit counter
• Specification
• Starting at zero, it increments by 3
• at 6, it wraps back to 0
• Has a reset signal input
• When reset=1, the next counter value is 0
• Uses D Flip-flops

reset

0

6

3

Counter ExampleUsing D FFs
• State Table
• Two different values of reset treated as different Next States in this example

reset=0 reset=1

Present

State

ABC

Next

State

ABC

Next

State

ABC

000

001

010

011

100

101

110

111

011

xxx

xxx

110

xxx

xxx

000

xxx

000

000

000

000

000

000

000

000

reset

0

6

3

Counter ExampleUsing D FFs

reset=0 reset=1

Present

State

ABC

Next

State

ABC

Next

State

ABC

XXX

XXX

0

Combina-

tionalLogic

output

(= state)

000

001

010

011

100

101

110

111

011

xxx

xxx

110

xxx

xxx

000

xxx

000

000

000

000

000

000

000

000

reset

DA,B,C

clk

reset

DA,B,C

XXX

output

XXX

reset

0

“current” time

6

3

Counter ExampleUsing D FFs

reset=0 reset=1

Present

State

ABC

Next

State

ABC

Next

State

ABC

000

XXX

1

Combina-

tionalLogic

output

(= state)

000

001

010

011

100

101

110

111

011

xxx

xxx

110

xxx

xxx

000

xxx

000

000

000

000

000

000

000

000

reset

DA,B,C

clk

reset

DA,B,C

XXX

000

output

XXX

XXX

reset

0

“current” time

6

3

Counter ExampleUsing D FFs

reset=0 reset=1

Present

State

ABC

Next

State

ABC

Next

State

ABC

011

000

000

0

Combina-

tionalLogic

output

(= state)

000

001

010

011

100

101

110

111

011

xxx

xxx

110

xxx

xxx

000

xxx

000

000

000

000

000

000

000

000

reset

DA,B,C

clk

reset

DA,B,C

XXX

000

011

output

XXX

XXX

000

reset

0

“current” time

6

3

Counter ExampleUsing D FFs

reset=0 reset=1

Present

State

ABC

Next

State

ABC

Next

State

ABC

110

011

0

Combina-

tionalLogic

output

(= state)

000

001

010

011

100

101

110

111

011

xxx

xxx

110

xxx

xxx

000

xxx

000

000

000

000

000

000

000

000

reset

DA,B,C

clk

reset

DA,B,C

XXX

000

011

110

output

XXX

XXX

000

011

reset

0

“current” time

6

3

Counter ExampleUsing D FFs

reset=0 reset=1

Present

State

ABC

Next

State

ABC

Next

State

ABC

000

110

0

Combina-

tionalLogic

output

(= state)

000

001

010

011

100

101

110

111

011

xxx

xxx

110

xxx

xxx

000

xxx

000

000

000

000

000

000

000

000

reset

DA,B,C

clk

reset

DA,B,C

XXX

000

011

110

000

output

XXX

XXX

000

011

110

reset

0

“current” time

6

3

Counter ExampleUsing D FFs

reset=0 reset=1

Present

State

ABC

Next

State

ABC

Next

State

ABC

011

000

0

Combina-

tionalLogic

output

(= state)

000

001

010

011

100

101

110

111

011

xxx

xxx

110

xxx

xxx

000

xxx

000

000

000

000

000

000

000

000

reset

DA,B,C

clk

reset

DA,B,C

XXX

000

011

110

000

011

output

XXX

XXX

000

011

110

000

reset

0

“current” time

6

3