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ECE3060
November 1, 2006
Homework #8 due Thursday October 19 @ 4:30pm
100 points
Solutions
1.
(20) Consider the following function: f = a’b’c’d’ + a’b’c’d + a’b’cd’ + a’b’cd + ab’c’d +
ab’cd’ + abc’d’ + abc’d + abcd’.
Use your favorite method to derive all possible prime
implicants for f.
For full credit, state which method you are using, show all work and
explain your work.
Also, state how many essential prime implicants you have found.
Using KMAP method:
7
prime implicants: a’b’, b’cd’, acd’, abd’, abc’, ac’d, b’c’d
1 essential prime implicant
: a’b’ (since a’b’c’d’ and a’b’cd are only covered by a’b’)
2.
(5) Design an A matrix for your answer to problem 1 above.
each row is a minterm of the function.
each column is a different prime implicant of the fuction.
if a minterm (row) is covered by a prime implicant (column), then that element is a 1
a'b’
b’cd’
acd’
abd’
abc’
ac’d
b’c’d
a’b’c’d’
1
0
0
0
0
0
0
a’b’c’d
1
0
0
0
0
0
1
a’b’c d’
1
1
0
0
0
0
0
a'b’c d
1
0
0
0
0
0
0
a b’c’d
0
0
0
0
0
1
1
a b’c d’
0
1
1
0
0
0
0
a b c’d’
0
0
0
1
1
0
0
a b c’d
0
0
0
0
1
1
0
a b c d’
0
0
1
1
0
0
0
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View Full Document3.
(35) For the following A matrix, use the QuineMcCluskey Exact 2Level Logic
Minimization algorithm taught in class to find the global minimum number of prime
implicants such that all minterms are covered.
Shown are the rows labeled m
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 Spring '07
 Shimmel

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