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 \(y\)?

  1. A.

    \(xy + x′ y′\)

  2. B.

    \(x\oplus y′\)

  3. C.

    \(x′\oplus y\)

  4. 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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