CSE140 – Fall 2006
Homework #3Solutions
For most of these problems, there is more than one approach.
It has been tried to show you several different approaches in different problems.
The
A
and
A’
forms are equivalent.
A
s in the textbook are written
A’
here.
1.
Problems 3.3 and 3.4
(b)
A
1
1
0
0
1
X
0
0
0
0
X
1
D
C
0
0
1
1
B
F(A,B,C,D) = AD+A’D’
Prime Implicants: AD, A’D’. Both are essential.
For each prime implicant, 1 don’t care is set to 1.
(c)
A
X
0
0
1
1
1
1
0
1
0
0
0
D
C
1
0
0
0
B
F(A,B,C,D) = A’B’+BC’D+B’C’D’
Prime Implicants corresponding to: A’B’, BC’D, B’C’D’, A’C’D
These prime implicants are essential: A’B’, BC’D, B’C’D’
For each of the two implicants corresponding to A’B’ and B’C’D’, 1 don’t care is
set to 1.
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CSE140 – Fall 2006
Homework #3Solutions
2.
Problem 3.5
(b)
A
1
0
0
0
1
0
1
1
1
0
0
0
D
C
0
0
0
1
B
F(A,B,C,D)=AC’D+AB’C’+A’B’D+AB’CD’
(c)
A
1
0
1
0
1
0
0
1
1
0
1
1
D
C
0
0
1
0
B
F(A,B,C,D)=A’B’C’+B’D+ABD’+ABC
(e)
A
1
1
0
0
1
0
0
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 Fall '06
 Rosing
 Prime number, Initialisms, XOR gate, xor b xor, xor C xor

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