Which of the following Boolean expressions is illustrated in the truth table's…
2017
Which of the following Boolean expressions is illustrated in the truth table's column F?
Answer: D. XY + X'Y' / XY + X'Y' — Correct Answer: XY + X'Y' Explanation: The truth table outputs 1 when X and Y are equal: (X,Y) = (0,0) -> 1 and (X,Y) = (1,1) -> 1. It outputs 0 when X and Y…
- A.
XY' + X / XY' + X
- B.
X'Y + XY' / X'Y + XY'
- C.
XY + XY' / XY + XY'
- D.
XY + X'Y' / XY + X'Y'
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Correct answer: D
Correct Answer: XY + X'Y'
Explanation:
The truth table outputs 1 when X and Y are equal: (X,Y) = (0,0) -> 1 and (X,Y) = (1,1) -> 1.
It outputs 0 when X and Y differ: (0,1) -> 0 and (1,0) -> 0.
The Boolean expression that is true when inputs are equal is the equivalence (XNOR) function, which can be written as XY + X'Y'.
Why the other common expressions are incorrect:
X'Y + XY' (exclusive OR) is true when X and Y are different, so it does not match the given table.
Expressions like XY + XY' or XY' + X both simplify to X, which outputs 1 whenever X = 1 regardless of Y, so they do not match the table either.
Conclusion: The table corresponds to XY + X'Y' (XNOR), so that expression is the correct representation of column F.