GATE EC 2014 Set 2 — Question 24
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Digital Circuits → Combinational Logic → K-Map Minimization
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Question
For an -variable Boolean function, the maximum number of prime implicants is
Correct answer
(D) 2⁽ⁿ⁻¹⁾
Solution
For an -variable Boolean function, the maximum number of prime implicants is . This occurs in functions where the minterms are arranged in a checkerboard pattern on the Karnaugh map (e.g., the XOR function), such that no two minterms are adjacent and each minterm itself becomes a prime implicant.
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