GATE CS 2017 Set 2 — Question 28
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Digital Logic → Boolean Algebra & Logic Gates → K-Map Minimization
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Question
Given , where represents the don't-care condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of ?
Correct answer
(A) f = (w + z)(x + z)
Solution
To find the minimum POS form, we group the zeros (Maxterms) and don't-cares in the K-map.Minterms:
Don't-cares:
Maxterms (0s): K-map for (grouping 0s):
Grouping 0s:
Don't-cares:
Maxterms (0s): K-map for (grouping 0s):
| 00 | 01 | 11 | 10 | |
|---|---|---|---|---|
| 00 | 1 | 1 | 1 | 1 |
| 01 | 0 | X | 1 | X |
| 11 | 0 | 0 | X | 0 |
| 10 | 1 | 0 | X | 1 |
1.Group 1: Maxterms 4, 12, 14 and Don't-cares 6. This covers . In POS form, this is .
2.Group 2: Maxterms 9, 13 and Don't-cares 11, 15. This covers . In POS form, this is .
Thus, the minimum POS form is .Continue learning with Success Tracker
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