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)?

  1. A.

    (A + B + C′)(A′ + B′ + C)(A + B′ + C)

  2. B.

    (A′ + B + C)(A + B + C′)

  3. C.

    (A′ + B + C)(A + B + C)(A + B + C)

  4. D.

    (A + B + C)(A + B + C′)(A′ + B + C)

  5. E.

    None of the above

Attempted by 28 students.

Show answer & explanation

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.

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