1) Two-level logic minimization (10 pts)
Consider the logic diagram shown below.
A
B
C
OR
F
0
1
0
1
0
1
B
D
B
C
D
a) Please fill out the following K-map for
F
as a function of
A
,
B
,
C
, and
D
.
1
1
1
1
00
01
11
10
CD
F
00
01
AB
1
1
1
1
1
1
11
10
b) For the K-map derived in part (a) for
F
, specify all the primes and essential primes.
Prime
Essential
1 - - 1
AD
- 1 - 1
BD
1 - 1 -
AC
X
- 1 1 -
BC
X
- - 0 1
¯
CD
X
c) Find the minimum two-level logic implementation for
F
.
F
=
AC
+
BC
+
¯
CD
2

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2) Number representation (10 pts)
a) For each binary vector below, what does it represent as an Octal number and a Hexadecimal
number?
Binary
Octal
Hexadecimal
00111110
076
3E
10100001
241
A1
00111001
071
39
b) Given
X
and
Y
below that are 5-bit numbers in 2’s complement form, fill in the table of what
S
should be bit-vector form (
even if the result causes an overﬂow
). Indicate whether or not
there is an
overﬂow
and what
S
is as a number (if
S
results in an overﬂow, then just put an ”x”
under the “
S
as a number” column). (First two rows provide examples.)
X
Y
S
=
X
−
Y
S
as a
x
4
x
3
x
2
x
1
x
0
y
4
y
3
y
2
y
1
y
0
s
4
s
3
s
2
s
1
s
0
Overﬂow?
number
11101
00011
11010
no
-6
00001
00111
11010
no
-6
11100
11001
00011
no
3
01000
10101
10011
yes
x
10110
00011
10011
no
-13
11000
01011
01101
yes
x
3