GATE CS 2018 Set 1 — Question 59
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Digital Logic → Boolean Algebra & Logic Gates → K-Map Minimization
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Question
Consider the minterm list form of a Boolean function given below.Here, denotes a minterm and denotes a don't care term. The number of essential prime implicants of the function is ______.
Correct answer
3 to 3
Solution
To find the Essential Prime Implicants (EPIs), we use a K-map for variables :
Prime Implicants (PIs):
| PQ \ RS | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
| 00 | 1 (0) | 0 (1) | X (3) | 1 (2) |
| 01 | 0 (4) | 1 (5) | 1 (7) | 0 (6) |
| 11 | X (12) | 0 (13) | 0 (15) | X (14) |
| 10 | X (8) | 1 (9) | 1 (11) | X (10) |
1.Quad (0, 2, 8, 10): . Minterm 0 is covered only by this PI. Thus, is an EPI.
2.Quad (8, 9, 10, 11): . Minterm 9 is covered only by this PI. Thus, is an EPI.
3.Pair (5, 7): . Minterm 5 is covered only by this PI. Thus, is an EPI.
4.Quad (2, 3, 10, 11): . Minterm 2 is also in , and minterm 11 is also in . It covers no unique minterm.
5.Quad (8, 10, 12, 14): . Covers only don't cares and minterms already covered.
The essential prime implicants are , , and . The count is 3.Continue learning with Success Tracker
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