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

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Solution

$f (A, B, C, D) = ¯ ¯¯¯¯¯¯ ¯ A B + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ C ¯ ¯¯¯ ¯ D + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ B D + ¯ ¯¯¯¯¯¯ ¯ A B C ¯ ¯¯¯ ¯ D = ¯ ¯¯¯¯¯¯ ¯ A B (1 + C ¯ ¯¯¯ ¯ D) + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ C ¯ ¯¯¯ ¯ D + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ B D = ¯ ¯¯ ¯ A + ¯ ¯¯ ¯ B + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ C ¯ ¯¯¯ ¯ D + ¯ ¯¯ ¯ A ¯ ¯¯ ¯ B D = ¯ ¯¯ ¯ A (1 + ¯ ¯¯ ¯ C ¯ ¯¯¯ ¯ D + ¯ ¯¯ ¯ B ¯ ¯¯¯ ¯ D) + ¯ ¯¯ ¯ B = ¯ ¯¯ ¯ A + ¯ ¯¯ ¯ B = ¯ ¯¯¯¯¯¯ ¯ A B$

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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)

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

R (A, B, C, D)

S_{1} = {A \to B, A B \to C, A C \to D, B \to C, B \to A}

S_{2} = {A B \to D, A C \to B, B \to D, B D \to C}

¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ (a + ¯ b + c + ¯ d) + (b + ¯ c)

H = {A \to B, B \to A, A B \to C, A C \to D, B \to C}

G = {C A \to B, B A \to D, B \to D, D B \to C}

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