The boolean expression Z = ĀB̄C̄D + ĀBCD̄ + AB̄C̄D + ABC̄D̄ can be minimized to?
2018
The boolean expression
Z = ĀB̄C̄D + ĀBCD̄ + AB̄C̄D + ABC̄D̄
can be minimized to?
Answer: B. Z = ĀBCD̄ + B̄C̄D + ABC̄D̄ — Given expression: Z = ĀB̄C̄D + ĀBCD̄ + AB̄C̄D + ABC̄D̄ These correspond to minterms m₁, m₆, m₉ and m₁₂. m₁ = ĀB̄C̄D and m₉ = AB̄C̄D differ only in A, so they…
- A.
Z = ĀBC + B̄C̄D + ABC̄D̄
- B.
Z = ĀBCD̄ + B̄C̄D + ABC̄D̄
- C.
Z = ĀBCD̄ + B̄D + BC̄D̄
- D.
Z = ĀBCD̄ + B̄C̄D + AB
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Correct answer: B
Given expression:
Z = ĀB̄C̄D + ĀBCD̄ + AB̄C̄D + ABC̄D̄
These correspond to minterms m₁, m₆, m₉ and m₁₂.
m₁ = ĀB̄C̄D and m₉ = AB̄C̄D differ only in A, so they combine as:
ĀB̄C̄D + AB̄C̄D = B̄C̄D
The minterms m₆ = ĀBCD̄ and m₁₂ = ABC̄D̄ do not have adjacent partners in the given function, so they remain unchanged.
Therefore,
Z = ĀBCD̄ + B̄C̄D + ABC̄D̄
Hence, option B is correct.