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A logic circuit provides the output Y as per the following truth table. The expression for the output Y is:
Notice Y is 1 when B=0, and Y is 0 when B=1 regardless of A -> Y = NOT(B) = B̄!
Examine the given truth table row by row: - Row 1: A = 0, B = 0 -> Y = 1 - Row 2: A = 0, B = 1 -> Y = 0 - Row 3: A = 1, B = 0 -> Y = 1 - Row 4: A = 1, B = 1 -> Y = 0
Writing the canonical minterms for the rows where the output Y is 1 (Row 1 and Row 3):
Factor out the common term B̄ using the distributive law:
Diagnose every choice: Know exactly why the right option works and why distractors fail.
Rigorous SOP Boolean reduction confirms Y = B̄.
Inverts the output; when B=0, Y=1, not 0.
For A=1, B=1, this expression gives 1 · 1 + 0 = 1, but truth table specifies Y=0.
For A=0, B=1, this expression gives 0 · 0 + 1 = 1, whereas the truth table gives Y=0.
Students spend time setting up complex Karnaugh maps without noticing that A is a "don’t care" redundant variable.
"When an output is high whenever a specific input is low and vice-versa regardless of other inputs, the function reduces to the single-variable NOT operation (Y = X̄)."
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