Which one of the following expressions does NOT represent exclusive NOR of…
20132013
Which one of the following expressions does NOT represent exclusive NOR of \(x\) and \(y\)?
Answer: D. \(x′\oplus y′\) — Key idea: exclusive NOR (XNOR) is true when x and y are equal; a standard form is xy + x′y′. Check the expression that does NOT match XNOR: For x′ ⊕ y′,…
- A.
\(xy + x′ y′\) - B.
\(x\oplus y′\) - C.
\(x′\oplus y\) - D.
\(x′\oplus y′\)
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Correct answer: D
Key idea: exclusive NOR (XNOR) is true when x and y are equal; a standard form is xy + x′y′.
Check the expression that does NOT match XNOR:
For x′ ⊕ y′, complementing both inputs gives x′ ⊕ y′ = x ⊕ y (property of XOR).
XOR (x ⊕ y) is 1 when x and y differ, while XNOR is 1 when x and y are equal, so x′ ⊕ y′ represents XOR, not XNOR.
Conclusion: x′ ⊕ y′ does NOT represent exclusive NOR; the other expressions (xy + x′y′, x ⊕ y′, x′ ⊕ y) are equivalent to XNOR.
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