Consider the Boolean expression: $f (A, B, C, D) = ¯ ¯¯¯¯¯¯ ¯ A B + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ C ¯ ¯¯¯ ¯ D + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ B D + ¯ ¯¯¯¯¯¯ ¯ A B C ¯ ¯¯¯ ¯ D$
then the minimised expression of $f (A, B, C, D)$ is equal to

¯ ¯¯¯¯¯¯ ¯ A B

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¯ ¯¯¯¯¯¯ ¯ B C

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¯ ¯¯¯¯¯¯¯ ¯ C D

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¯ ¯¯¯¯¯¯ ¯ A C

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Solution

The correct option is A $¯ ¯¯¯¯¯¯ ¯ A B$
$f (A, B, C, D) = ¯ ¯¯¯¯¯¯ ¯ A B + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ C ¯ ¯¯¯ ¯ D + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ B D + ¯ ¯¯¯¯¯¯ ¯ A B C ¯ ¯¯¯ ¯ D = ¯ ¯¯¯¯¯¯ ¯ A B (1 + C ¯ ¯¯¯ ¯ D) + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ C ¯ ¯¯¯ ¯ D + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ B D = ¯ ¯¯ ¯ A + ¯ ¯¯ ¯ B + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ C ¯ ¯¯¯ ¯ D + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ B D = ¯ ¯¯ ¯ A (1 + ¯ ¯¯ ¯ C ¯ ¯¯¯ ¯ D + ¯ ¯¯ ¯ B ¯ ¯¯¯ ¯ D) + ¯ ¯¯ ¯ B = ¯ ¯¯ ¯ A + ¯ ¯¯ ¯ B = ¯ ¯¯¯¯¯¯ ¯ A B$

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Similar questions

f (A, B, C, D) = (A + B + C + ¯ D) (A + ¯ B + ¯ C + D) (A + B + ¯ C + ¯ D) (¯ A + ¯ B + ¯ C + ¯ D) (¯ A + ¯ B + ¯ C + D)

f (A, B, C, D)

$F (A, B, C, D) = B ¯ ¯¯¯ ¯ D + ¯ ¯¯ ¯ B C D + A B C + A B ¯ ¯¯ ¯ C D + ¯ ¯¯ ¯ B ¯ ¯¯¯ ¯ D$

- N O_{2}

- N H ­_{2}

∣ ∣ ∣ ∣ ∣ \begin{matrix} 2 & a + b + c + d & a b + c d a + b + c + d & 2 (a + b) (c + d) & a b (c + d) + c d (a + b) a b + c d & a b (c + d) + c d (a + b) & 2 a b c d \end{matrix} ∣ ∣ ∣ ∣ ∣

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 2 & a + b + c + d & a b + c d a + b + c + d & 2 (a + b) (c + d) & a b (c + d) + c d (a + b) a b + c d & a b (c + d) + c d (a + b) & 2 a b c d \end{matrix} ∣ ∣ ∣ ∣ ∣

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