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Consider the following multiplexer where $I0, I1, I2, I3$ are four data input lines selected by two address line combinations $A1A0=00,01,10,11$ respectively and $f$ is the output of the multiplexor. EN is the Enable input.

The function $f(x,y,z)$ implemented by the above circuit is

- $xyz'$
- $xy + z$
- $x + y$
- None of the above

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## 2 Answers

Best answer

As $x$ is connected to $I0$ & $I1$, $y$ connected to $I2,$ $y'$ connected to $I3$ & $A1,$ $z$ connected to $A0$ and $z'$ connected to ENABLE $(EN),$

$f= ( {\overline{A1}}.{\overline{A0}}.I0+ {\overline{A1}}.A0.I1 +A1.{\overline{A0}}.I2 + A1.A0.I3 ).EN$

$\implies f = (xyz' +xyz + y'z'y + zy')z'$

$\qquad= (xyz' +xyz + zy')z' =xyz'$

Correct Answer: $A$

$f= ( {\overline{A1}}.{\overline{A0}}.I0+ {\overline{A1}}.A0.I1 +A1.{\overline{A0}}.I2 + A1.A0.I3 ).EN$

$\implies f = (xyz' +xyz + y'z'y + zy')z'$

$\qquad= (xyz' +xyz + zy')z' =xyz'$

Correct Answer: $A$