UC Davis
1
Hussain AlAsaad
U
NIVERSITY
OF
C
ALIFORNIA
—D
AVIS
D
EPARTMENT
OF
E
LECTRICAL
& C
OMPUTER
E
NGINEERING
EEC180A—D
IGITAL
S
YSTEMS
I
F
ALL
2001
M
IDTERM
II
S
TUDENT
I
NFORMATION
I
NSTRUCTIONS
The exam is closed book and notes.
Print your name and your ID number.
Circle your lab section number(s).
There are five problems in the exam. Solve all of them and show your work.
If you need more space for your solution, use the back of the sheets.
E
XAM
G
RADE
Name
Hussain AlAsaad
ID Number
xxxxxxxxx
Lab
Section
Registered
A01
(M 711pm)
A02
(T 711pm)
A03
(W 711pm)
A04
(R 711pm)
A05
(F 711pm)
A06
(M 711am)
A07
W 711am)
Attending
A01
(M 711pm)
A02
(T 711pm)
A03
(W 711pm)
A04
(R 711pm)
A05
(F 711pm)
A07
(W 711am)
None
Problem
Maximum
Points
Student
Score
1
20
20
2
30
30
3
20
20
4
20
20
5
10
10
Total
100
100
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UC Davis
2
Hussain AlAsaad
1. A
RITHMETIC
C
IRCUITS
(20
POINTS
)
Design a gatelevel circuit
C
that computes the function
, where the input
X
is a 3
bit two’s complement number represented by
X
2
X
1
X
0
and the output
Y
is a 5bit two’s complement
number represented by
Y
4
Y
3
Y
2
Y
1
Y
0
. Minimize the number of gates in your design. Assume that the
input combination
X
2
X
1
X
0
= 100 will never appear at the inputs of
C
. Moreover, you can assume
that the literals and their complements are available.
The above solution requires four logic gates. In fact there exist a solution with three logic
gates. This can be obtained by some logic manipulation of the
Y
3
equation as follows:
By using the above equation, we can implement the circuit
C
using three gates (two AND and
one XOR).
2. F
LIPFLOPS
(10 + 10 + 10 = 30
POINTS
)
In this problem, you are to analyze a new type of flipflop, the
XY
flipflop. The description of
the
XY
flipflop is given below.
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 Spring '08
 REDINBO
 State transition table

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