Flip-Flops Assume the an edge-triggered flip-flop FF implements a - - PowerPoint PPT Presentation

SLIDE 1

Flip-Flops

• An edge-triggered flip-flop is not a combinational circuit.

Proof: Every combinational circuit implements a Boolean function. We show that an edge-triggered flip-flop is not an implementation

• f any Boolean function.

Assume the an edge-triggered flip-flop FF implements a Boolean function f with propagation delay tpd(f ) . Claim: An edge-triggered flip-flop is not a combinational circuit.

• f

t CLK

pd

• 2
• For CLK = 0 and D = 0, f(0,0) = Q = 1.

For CLK = 0 and D = 0, f(0,0) = Q = 0.

i

C

i

A

1

• i

C

1

• i

A

f t pd 1

CLK t D t Q

• FF doesn’t implement any Boolean function.
• FF is not a combinational circuit.

f t pd

FF

i

INV 2 FF’ t D t D

• '

t Q' t Q

Overcoming non-empty intersection of Ci and Ai

cont hold

t t FF

• :
• :
• INV

CONT INV

• cont

hold j

t t INV CONT j i

• 2

min

su su

t t

• hold

hold

t t

• INV

CONT i t t

cont cont

• 2
• INV

PD i t t

pd pd

• 2

SLIDE 2

• MUX

PD t t

su su

• MUX

CONT t t

hold hold

• cont

cont

t t

• pd

pd

t t

• i

C

i

A

CLK t CE t D , t Q t DFF

CONT(MUX) PD(MUX)

Clock enabled edge-triggered flip-flop

MUX FF t D t CE CLK t Q

Definition: An edge-triggered flip-flop with a reset signal is defined as follows: . clock a and , signals Digital : Inputs CLK t RST t D

.

signal Digital : Output t Q

• cont

i pd i i

t t t t t C t RST t D

• 1

, every for then , segment critical the during stable are and If : ity Functional

• 1

if if

i i i

t RST t RST t D t Q

An edge-triggered flip-flop with a reset signal

MUX FF t D t RST CLK t Q

Changing the flip-flop parameters (0)

FF t Q t D CLK

• ,
• FF

t FF t

hold su

G

• G

t G t

cont pd

i

G A concatenation of i G gates:

• G

t i G t

pd i pd

• G

t i G t

cont i cont

• Goal:

(1) Design an edge-triggered flip-flop FF’ with thold(FF)

• 0.

(2) Design an edge-triggered flip-flop FF’’ with tsu(FF)

• 0.

FF

i

G FF’ t D' t Q t Q

• '

t D

CLK

• G

t i FF t F F t

pd su su

• G

t i FF t F F t

cont hold hold

• FF

t F F t

cont cont

• FF

t F F t

pd pd

• G

t FF t i

cont hold

• F

F thold

Changing the flip-flop parameters (1)

SLIDE 3

Changing the flip-flop parameters (2)

• G

t i FF t F F t

cont su su

• G

t i FF t F F t

pd hold hold

• G

t i FF t F F t

cont cont cont

• G

t i FF t F F t

pd pd pd

• CLK

CONT(Gi) PD(Gi) CONT(Gi) PD(Gi)

X

• G

t FF t i

cont su

• F

F tsu

FF

i

G FF’’

t Q t Q

• t

D t D

• CLK

X