The output of the following combinational circuit is :
2016
The output of the following combinational circuit
is :
- A.
\(X . Y\) - B.
\(X + Y\) - C.
\(X \oplus Y\) - D.
\(\overline {X \oplus Y}\)
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Correct answer: D
Key idea: identify each gate output and simplify the Boolean expression.
Top left gate: inputs are inverted before entering a NAND (input bubbles) and the gate has an output bubble, so its function is NAND(NOT X, NOT Y) = X + Y (OR).
Bottom left gate: a standard NAND of X and Y, so its output is NAND(X, Y) = NOT(XY).
Rightmost gate: a NAND taking the two previous outputs. If A = NOT(XY) and B = X + Y, the final output is NAND(A, B) = NOT(A · B).
Algebraic simplification:
Let A = NOT(XY) and B = X + Y. Then the internal product is A · B = NOT(XY) · (X + Y). Distribute and simplify:
NOT(XY) · (X + Y) = X·NOT(Y) + Y·NOT(X) which is exactly X XOR Y.
The final output is NOT(A · B) = NOT(X XOR Y), i.e. X XNOR Y.
Conclusion: the circuit implements the negation of XOR, commonly written as X XNOR Y or overline{X ⊕ Y}.