GATE EC 2024 Set 1 — Question 19
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Digital Circuits → Combinational Logic → K-Map Minimization
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Question
For the Boolean function , the essential prime implicants are __________.
Correct answer
(A) BD, BD
Solution
To find the essential prime implicants (EPIs), we first identify all prime implicants (PIs) using a K-map for the given minterms: .1. Identify Prime Implicants (PIs):
A prime implicant is essential if it covers at least one minterm that is not covered by any other prime implicant.
- Group 1:
- Group 2:
- Group 3:
- Group 4:
A prime implicant is essential if it covers at least one minterm that is not covered by any other prime implicant.
- Minterms and are covered only by . Thus, is an EPI.
- Minterms and are covered only by . Thus, is an EPI.
- Minterm is covered by and .
- Minterm is covered by and .
- Minterm is covered by and .
- Minterm is covered by and .
- Minterm is covered by and .
- Minterm is covered by and .
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