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A four-variable Boolean function is realized using $4\times 1$ multiplexers as shown in the figure.

The minimized expression for $\text{F(U,V,W,X)}$ is 

  1. $\left ( UV+\overline{U}\:\overline{V}\right )\overline{W}$
  2. $\left ( UV+\overline{U}\:\overline{V}\right )\left (\overline{W}\: \overline{X}+\overline{W}\:X\right )$
  3. $\left ( U\:\overline{V}+\overline{U}\:V\right )\overline{W}$
  4. $\left ( U\:\overline{V}+\overline{U}\:V\right )\left (\overline{W}\: \overline{X}+\overline{W}\:X\right )$
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$V_{CC}$ is Voltage Common Collector, generally represents the Higher Voltage with respect to $GND$ (Ground)

$GND$ (Ground) is usually a reference point ( $0V$) for a electronic circuits, and in general $Vcc$ is taken as $+5V.$

So, due to higher voltage w.r.t Ground, $V_{CC} = 1$

So, $I_{1}$ and $I_{2}$ is connected with $1$

 

So, First MUX output will be: $U’V + UV’ $ and this is the Input of Second MUX’s $I_{0}$ and $I_{1}$

Now, $F\ (U, V, W, X) = (U’V + UV’). W’X’ + (U’V + UV’). W’X $

                                           $= (U’V + UV’).( W’X’  + W’X) $

                                           $= (U’V + UV’).W’$ 

 

[ Note $:$ $I_{0} , I_{3}$ MUX-1 and $I_{2} , I_{3}$ are connected with Ground i.e Voltage 0, so we didn’t include those in calculation.]

 

$Ans: Option \ C$

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