Edge-triggered Flip-Flop, State Table, State Diagram

Edge-triggered Flip-Flop • Contrast to Pulse-triggered SR Flip-Flop

• Pulse-triggered: Read input while clock is 1, change output when the clock goes to 0. What happens during the entire HIGH part of clock can affect eventual output.

• Edge-triggered: Read input only on edge of clock cycle (positive or negative) • Example below: Positive Edge-Triggered D Flip-Flop

• On the positive edge (while the clock is going from 0 to 1), the input D is read, and almost immediately propagated to the output Q. Only the value of D at the positive edge matters.

D

C

S

C

R

D

Clock

Q

Q

Symbol

• Symbol of edge-triggered D flip-flop

D

C

D

C

Positive-edge triggered Negative-edge triggered

Flip-Flop Timing

• Set-up time: ts • Input needs to be stable before trigger

• Hold time: th • Input needs to be stable after trigger

• Propagation delay: tp • Some delay from trigger to output change

• Example: Negative edge triggered flip-flip

Clock

ts th

tp

Sequential Circuit Description

• Input Equations

• State Table

• State Diagram

• We’ll use the following example

Sequential Circuit Description

D

C

D

C

Clock

X A

A

B

B

Y

Sequential Circuit Description

D

C

D

C

Clock

X A

A

B

B

Y

input

output

Next state Present state

At the clock trigger, the next state

will be read and transferred to the

present state

Input Equations

Anext = ApresentX + BpresentX

Bnext = A’presentX

Y = (Apresent + Bpresent)X’

Next state in terms of

input and present state

Output in terms of input

and present state

State Table

Present State Input Next State Output

A B X A B Y

0 0 0 0 0 0

0 0 1 0 1 0

0 1 0 0 0 1

0 1 1 1 1 0

1 0 0 0 0 1

1 0 1 1 0 0

1 1 0 0 0 1

1 1 1 1 0 0

State Diagram

00 01

11 10

0/0 1/0

0/1

1/0 0/1

1/0

1/0

0/1

Mealy and Moore Models

• Preceding Example: Output depends on present state and input. This is called the Mealy Model

• Another kind of circuit: Output only depends on present state. This is called the Moore Model

Example of Moore Model X

Y D

C

Clock

A Z

Anext = Apresent + XY

Z = Apresent

0/0 1/1

X Y Apresent Anext

0 0 0 0

0 0 1 1

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1

00,01,10 11

00,01,10,11

Moore Model

Some

Combinational

Circuit Outputs

Inputs Some

Combinational

Circuit

Flip-flops

Mealy Model

Some

Combinational

Circuit Outputs

Inputs Some

Combinational

Circuit

Flip-flops

Mealy and Moore Model State Diagrams

00 01

11 10

0/0 1/0

0/1

1/0 0/1

1/0

1/0

0/1

0/0 1/1

00,01,10 11

00,01,10,11

Moore

input

state output

input

output

state

How to Design a Sequential Circuit

• 1. Specification

• 2. Formulation: Draw a state diagram

• 3. Assign state number for each state

• 4. Draw state table

• 5. Derive input equations

• 5. One D flip-flop for each state bit

Example

• Design a sequential circuit to recognize the input sequence 1101.

• That is, output 1 if the sequence 1101 has been read, output 0 otherwise.

A B C D

0/0

1/0 1/0

1/0

0/0

0/0 1/1

0/0

Assign States

• 4 states, so we need 2 bits

00 01 10 11

0/0

1/0 1/0

1/0

0/0

0/0 1/1

0/0

State Table

Present State Input Next State Output

A B X A B Y

0 0 0 0 0 0

0 0 1 0 1 0

0 1 0 0 0 0

0 1 1 1 0 0

1 0 0 1 1 0

1 0 1 1 0 0

1 1 0 0 0 0

1 1 1 0 1 1

Input Equations

Anext = A’BX + AB’

Bnext = A’B’X + AB’X’ + ABX

Y = ABX

Circuit Diagram

D

C

D

C

Clock

X A

A

B

B

Y

Exercise:

Fill in the input to

Flip-Flop B