ECE 349
Homework Assignment #10
Solutions
1. (3 points) Do sample problem 1.c from the State Machine timing handout.
SM Clock
(Clock)’
TpFFmax (35)
TpComb max (44)
Tsetup min (10)
TpInv min (6)
Tclk/2 + 6 = 89 ns
Tclk = 83 ns
F max = 6.024 MHz
2. (3 points) Do sample problem 1.d from the State Machine timing handout.
SM Clock
Delayed Clock
TpFFmax (35)
TpComb max (44)
2 (TpInv max) (26)
Tsetup min (10)
Tclk min = 89 + 26 = 115 ns F max = 8.7 MHz
3. (3 points) Do sample problem 3.c from the State Machine timing handout.
Input Clock
SM Clock
250 ns
TpOut min = 250 + 67 - 6 = 311 nsec
i.
Rising edge on
Output reg.
311/6 = 52 inverters
ii. 61 ns required from clock on input reg. to output reg. clock: 61/6 = 11 inverters
4. (3 points) The circuit below is commonly used as an asynchronous input synchronizer
for a synchronous circuit such as a state machine (X is the asynchronous input). If
tpF F max = 10 nsec, tSET U P min = 5 nsec, and tHOLDmin = 3 nsec for each flip-flop,
determine the maximum clock frequency for the circuit.
Answer: 40 MHz. This is for the path between flip-flops S and T.
X
D
Q
D
Q
D
Q
(R)
(S)
(T)
CK
CK
CK
D
Q
(U)
Q
CK
CLOCK
5. Assuming the same timing parameters as in the previous problem, consider the circuit
below. You should find that it may not work properly at any frequency. Explain why.
Answer: Depending on the exact propagation delay of flip-flops U and R, either the
setup or the hold time for flip-flop S may not be met. For example, flip-flop R has an
exact propagation delay of 8 nsec and flip-flop U has an exact propagation delay of 10
nsec, a setup time violation will occur at flip-flop S. If the two delays are reversed, a
hold time violation will occur at flip-flop S.
X
D
Q
D
Q
D
Q
(R)
(S)
(T)
CK
CK
CK
D
Q
(U)
CLOCK
Q
CK
6. Do sample problem 4.a from the State Machine timing handout.
The transition from state d to state a can cause a glitch on outputs W and V . The
transition from state b to state d can cause a glitch on output W .
7. (3 points) Do sample problem 4.b from the State Machine timing handout.
AB
C
00
01
11
10
V
0
a
c
1
b
e
f
W
V,W
X
X
d
Also OK to exchange entries (d & X) in 10 column
8. (Optional, 3 points) Hand the homework in on time and receive 3 points.