# Old midterm #2 sol ```First Name:
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CSE 140 Midterm 2
Tajana Simunic Rosing
Winter 2012
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Do not start the exam until you are told.
Write your name and PID at the top of
every page. Do not separate the pages.
Turn off and put away all your
electronics.
This is a closed-book, closed-notes, nocalculator exam. You may only refer to
one 8 &frac12; x 11” page of your handwritten
notes.
Do not look at anyone else’s exam. Do
not talk to anyone but an exam proctor
during the exam.
If you have a question, raise your hand
and an exam proctor will come to you.
You have 80 minutes to finish the exam.
When the time is finished, you must
stop writing.
provided.
To get the most partial credit, clearly
and neatly show all steps of your work.
1. 10 points
2. 15 points
3. 15 points
4. 15 points
5. 20 points
6. 25 points
Total (100 pts.)
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Problem 1
Consider the following circuit with a NOR-based SR-latch that is sensitive to high level
of clock. Timing information is as follows:
Tlatch
= 0.5 ns
Tgate
= 0.5 ns
Clock period = 4 ns with 50% duty cycle
a) Draw the output waveforms for Q, Q’, X, Y, Z, and OUT from t=0 to t=7
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b) Identify and name (static-0, static-1, dynamic) any hazards in the above waveforms.
The 101 glitch at t=2ns to t=2.5ns is a static-1 hazard.
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Problem 2
Answer the following questions assuming given information below. Signal IN is an input
to the circuit, and OUT is an output from the circuit.
Tsetup = 1 ns
Thold = 1 ns
Tpd
= 2 ns
Tgate = 2 ns
D Q
CLK
IN
D Q
CLK
D
Q
OUT
CLK
a) What is the minimum clock period for this circuit assuming delay from IN is zero?
The critical path is from the lower left FF to the right right FF through two XOR gates
and two NAND gates. Total delay is Tpd + TXOR + TXOR + TNAND + TNAND + Tsetup = 11ns.
Thus the minimum clock period is 11ns.
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b) Is it possible to increase the clock frequency by modifying the circuit without changing
its functionality? If so, show how can this be achieved, and calculate what would the
clock period be. If not, clearly explain why not.
The circuit is in fact a synchronous Mealy FSM design, and the combinations logics
compute both the next state and output value (which is registered for one cycle). The
circuit can be modified into a Moore FSM design, which would exhibit same
functionality and timing behaviors as synchronous Mealy. In order to do this, the input to
the upper right NAND can be moved to the output of the left registers, and the right
register can be removed. This would reduce the critical path to 2 gates (either two XOR
or two NANDs). In this case, the minimum clock period is 7ns.
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Problem 3
Draw a state transition diagram for the circuit below. Succinctly describe what the circuit
does. Signal IN is an input to the circuit.
The state transition diagram is as below. It’s a grey code counter, where it counts up
when IN=1, and maintains value on IN=0.
0
A=0
B=0
1
1
0
A=0
B=1
A=1
B=0
1
1
A=1
B=1
0
0
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Problem 4
Draw a state transition diagram for FSM that counts the cumulative number of 1’s in 2bit input sequence, and outputs 1 if it is a multiple of 3, and 0 otherwise. For example:
00  11  10  01  00  …
1 0 1 0 0  …
Input:
Output:
You must not use more than 4 states.
00/1
mod 3
=0
01,10/1
01,10/0
11/1 11/0
11/0
00/0
mod 3
=1
mod 3
=2
01,10/0
00/0
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Problem 5
Below is a FSM for a 2-bit saturating counter, commonly used as a simple hardware
predictor. Design a circuit for the 2-bit saturating counter. Use minimum number of DFFs and as few gates as possible.
Because the states transitions are only to two other states, it might be best to encode
states in grey code. Lets say S0 = 00, S1=01, S2=11, S3=10
In
0
0
0
0
1
1
1
1
CS
0
0
1
1
0
0
1
1
Out = CS
NS = CS CS’ + CS In
NS = In XOR CS
CS
0
1
0
1
0
1
0
1
Out
0
0
1
1
0
0
1
1
NS
0
0
1
0
0
1
1
1
NS
0
0
1
1
1
1
0
0
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Problem 6
Answer the following questions for the following state transition diagram.
a) Fill in the state transition table below
Current state
S0
S1
S2
S3
S4
S5
Next state
Input = 0
S2
S4
S1
S1
S2
S4
Output
Input = 1
Input = 0
Input = 1
S1
1
0
S3
1
1
S0
0
0
S4
0
0
S5
1
0
S2
1
1
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b) Fill in the implication table
X
X
X
S1-S5
X
X
X
S0-S4
X
X
X
S2-S3
X
X
X
c) List all the original states, grouped into maximal classes of compatibility. Use only as
many groups as necessary.
g0 = {S1, S5}
g1 = {S2, S3}
g2 = {S0, S4}
g3 =
g4 =
g5 =
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d) Identify a set that satisfies both covering and closure conditions on maximal class of
compatibility. List the resulting state transition and outputs in the table. Fill in as many
rows of the table as necessary.
Current state
g0
g1
g2
g3
g4
g5
Next state
Input = 0
g2
g0
g1
Output
Input = 1
Input = 0
Input = 1
g1
1
1
g2
0
0
g0
1
0
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