Discussion
The output f of the 4-to-1 Mux shown in the given figure is
Answer: B
The multiplexer output is \(x + y\) (option B). Data inputs 1, 2 and 3 are tied to \(V_{CC}\) (logic 1) and input 0 is grounded (logic 0), so the output is 0 only when the select lines choose input 0, that is x = 0 and y = 0, and it is 1 for every other combination. That is the OR function.
\[ f = \overline{x}\,\overline{y}\cdot 0 + \overline{x}y\cdot 1 \]
\[ \quad + x\overline{y}\cdot 1 + xy\cdot 1 = x + y \]
Options A and C are 1 for most or all inputs, and option D, \(x\overline{y}\), is 1 for only one combination, so none of them matches the OR behaviour.
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