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The number of min-terms after minimizing the following Boolean expression is _______.

[D'+AB'+A'C+AC'D+A'C'D]'
in Digital Logic by Veteran (105k points)
edited by | 4.8k views
+4
Directly apply the boolean algebra and get the right answer

min-term=1
0

15 max terms

1 min terms 

11 Answers

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by Loyal (5.3k points)
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Plot all the terms on a K-map and you'll get this. (Excuse the crap paint skills)

The final expression is the complement of this. So, focus on empty cells. There's just one.

Each cell represents a min-term, hence, we got just 1 min-term.

 

by Loyal (6.5k points)
0 votes

[D'+AB'+A'C+AC'D+A'C'D]'

After applying complementation on given expression we get

>>D(A'+B)(A+C')(A'+C+D')(A+C+D')

>>(A'D+BD)(A+C')(A'+C+D')(A+C+D')

>>(A'AD+A'C'D+ABD+BC'D)(A'A+A'C+A'D'+AC+C+CD'+AD'+CD'+D')

>>(0+A'C'D+ABD+BC'D)(0+A'C+A'D'+AC+C+CD'+AD'+CD'+D')

>>(A'C'D+ABD+BC'D)(A'C+AC+CD'+C+AD'+A'D'+D')   

>>(A'C'D+ABD+BC'D)(C+D')  

>>ABCD only minterm

 

by (131 points)
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