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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

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

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

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

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

- 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

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

- 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

- 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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