Delays in latches
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R. Q. P. S. Delays in Latches. A latch is a pair of cross-coupled inverters They can be NAND or NOR gates as shown Consider their behavior (each step is one gate delay in time) From R and S to P and Q stable condition is reached in three gate delays. R. S. Q. P. D. D. Q. Q. D. P.

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Delays in latches l.jpg

R

Q

P

S

Delays in Latches

  • A latch is a pair of cross-coupled inverters

    • They can be NAND or NOR gates as shown

    • Consider their behavior (each step is one gate delay in time)

    • From R and S to P and Q stable condition is reached in three gate delays

R

S

Q

P


Delays in gated latch and flip flops l.jpg

D

D

Q

Q

D

P

P

G

G

C

R

R

R

Q

Q

Q

D

Q

D

P

P

P

D

D

D

S

S

S

G

P

G

G

G

C

Delays in Gated-Latch and Flip-Flops

  • G acts as a control signal in a gated latch

    • G = 0 means no writing, G = 1 allows writing

  • In an edge-triggered flip-flop, data is written in flip-flop upon arrival of a clock edge

  • This is achieved by connecting two gated latches as shown

  • Actual implementation may be slightly different, concept is same


Timing issues in d flip flops l.jpg

R

R

Q

Q

D

P

P

D

D

S

S

G

G

C

Timing Issues in D Flip-flops

  • When C is low, second gated latch does not record anything, but the first latch samples the D-input

  • Before the clock changes from low to high

    • Changes in D propagate through many gates to output. Therefore D should be stable for at least five gate delays

    • This represents the set up time of a flip flop

  • When clock changes from low to high

    • The first latch may still sample up to two gate delay time. Therefore, D should remain stable even after clock changes

    • This is called the hold time of a flip flop


Timing in a state machine l.jpg

O

U

T

P

U

T

S

Next

State

Logic

Output

Logic

I

N

P

U

T

S

Timing in a State machine

  • The blocks of a Moore machine are shown below

  • Next state logic determines the next state based on current state and next input

  • Output logic determines the output based on current state

  • From rising edge, stored state is stable after four gate delays

  • Next state logic may take 2 or more gate delay worth of time

    • This is called contamination time, the minimum time taken for output to change after input changes

  • And then input to latches must remain stable for set up time


Example l.jpg

S0

S1

S2

S3

Example

  • Consider a four states system

  • State transition table, implementation level state transition table, output table, and implementation level output tables are

  • Using the logic equations below, combination logic takes two gate delay

L2 = XY’+XY = X X := X’Y+XY’

L1 = X’Y+XY = Y Y := X’Y’+XY’ = Y’

L0 = X’Y’+X’Y+XY’+XY = X’+X = 1


Recap all delays l.jpg
Recap All Delays

  • A combination circuit has

    • Contamination delay (tcd) -- Minimum delay before output starts to change 2 to 3 gate delays (depends on # of levels)

    • Propagation delay (tpd) -- Maximum delay after which all outputs are stable once input change

  • A flip-flop has set up time -- about 5 gate delay

  • A flip-flop has hold time -- minimum time for which input to latch should not change after a clock edge -- about 2 gate delay

  • A flip-flops propagation delay is time from clock edge to time at which its output is stable.

  • Clock low time > set up time

  • Clock high time > FF Prop

  • Clock time > FF Prop +

    compute + set up time

FF Propagation Time

FF Set up Time

Compute Time

FF Hold Time


Clock cycles l.jpg

Tcd = 2

Tpd = 5

Tcd = 2

Tpd = 5

Tcd = 2

Tpd = 5

Tcd = 2

Tpd = 5

Tcd = 2

Tpd = 8

Tcd = 5

Tpd = 10

Tcd = 2

Tpd = 5

Clock Cycles

  • Computing contamination delay (tcd) and propagation delay (tpd) of a combinational circuit

    • It depends on various paths in the circuit

    • We need to find the shortest path for contamination and longest path for propagation

  • For the circuit given below

    • Contamination delay = ….

    • Propagation delay = …..

  • Clock cycle time must allow for propagation delay of circuit, set up time of FF, and propagation time of FF

  • Contamination time of combinational circuit must be lower than hold time of FF


Speed of the circuit and clock frequency l.jpg
Speed of the circuit and clock frequency

  • Clock cycles are determined based on timing considerations

  • Circuit runs at clock speed of f

  • Corresponding clock cycle time (period) is T = 1/f

  • Or f = 1/T

  • A frequency of 1MHz gives a clock cycle time of 1 micro second

  • A frequency of 500MHz gives a clock period of 2 nano second

  • Let

    • T be the clock period

    • tpd be the propagation time of combinational circuit

    • tcd be the contamination time of combinational circuit

    • trd be the propagation time of FF (register) circuit

    • tst be the set up time of FF (register) circuit

    • tht be the hold time of FF (register) circuit


Some relationships in state machine times l.jpg
Some Relationships in state machine times

  • What is the minimum clock period?

    • T = tpd + trd + tst

  • By how long must any change in external inputs precede the next clock edge?

    • tpd + tst

  • How long after the clock edge must the external inputs be held valid?

    • tht - tcd

  • what is the smallest time after the clock edge that external outputs can be expected to be valid?

    • trd + tpd


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