What is the POS form of the Boolean expression F(A, B, C) = Π(1, 2, 4, 6)?
2025
What is the POS form of the Boolean expression F(A, B, C) = Π(1, 2, 4, 6)?
- A.
(A + B + C′)(A′ + B′ + C)(A + B′ + C)
- B.
(A′ + B + C)(A + B + C′)
- C.
(A′ + B + C)(A + B + C)(A + B + C)
- D.
(A + B + C)(A + B + C′)(A′ + B + C)
- E.
None of the above
Attempted by 28 students.
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Correct answer: E
Given F(A, B, C) = Π(1, 2, 4, 6).
Π denotes the product of maxterms, so the canonical POS form must include the maxterms M₁, M₂, M₄, and M₆.
For a maxterm:
Binary 0 -> variable without complement
Binary 1 -> complemented variable
M₁: 1 = (001)₂ -> A + B + C′
M₂: 2 = (010)₂ -> A + B′ + C
M₄: 4 = (100)₂ -> A′ + B + C
M₆: 6 = (110)₂ -> A′ + B′ + C
Therefore,
F = (A + B + C′)(A + B′ + C)(A′ + B + C)(A′ + B′ + C)
None of the original options A-D contains all four required maxterms exactly. Therefore, the correct answer is option E: None of the above.