g = (1 and x1’) or (0 and x1)

g = x1’

f = ac’ + bc

f = (a and x2′) or (b and x2)

f = (g and x2′) or (x1 and x2)

f = x1’x2’ + x1x2

Ref: Geeksforgeeks.org

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$\underline{\textbf{Answer:}\Rightarrow}$

$\underline{\textbf{Explanation:}\Rightarrow}$

A multiplexer has $\mathbf 3$ things:

- Selection Line.
- Input Line.
- Output Lines.
- For $\mathbf{2:1}$ Multiplexer, there are $\mathbf 2$ inputs and $\mathbf 1$ output and $\mathbf 1$ selection line.

So, when Selection Line, $\mathbf {X_1}$ is set $\mathbf 0$, then $\mathbf {a}$ will be selected and when $\mathbf {X_1 = 1}$, then $\mathbf b$ will be selected.

$\therefore $ Equation will be: $\mathbf{g = 1.X_1' + 0.X_1 = X_1'}$

Now, this $\mathbf{g = X_1}$ will be given as input to second multiplexer.

Following the same procedure for second multiplexer and taking one input as $\mathbf{X_1'}$, we will get:

$\mathrm{f = X_2'X_1' + X_2X_1}$

$\therefore \mathbf C$ is the correct answer.

edited
Oct 26, 2020
by arpit_18

A silly doubt: How do we consider multiplying the select line inputs like, why X1’ *1 and not X1’*0?

As input is given as 0 in a and 1 in b. Corresponding to that the select line should be taken, right? Please help me with this doubt.

Just I need to know that why didn’t you multiplied X1’ with 0. As input is zero so select line has to be complemented, please correct me if I’m wrong.

As input is given as 0 in a and 1 in b. Corresponding to that the select line should be taken, right? Please help me with this doubt.

Just I need to know that why didn’t you multiplied X1’ with 0. As input is zero so select line has to be complemented, please correct me if I’m wrong.

$f=ac'+bc$

Now, solve without considering $X1,X2,1,0$ and try to get function $f.$

Output of $mux_{1}:$ $g=c'a+cb$ and

Output of $mux_{2}:$ $c'g+cb\Rightarrow c'(c'a+cb)+cb=c'a+cb=$ $ac'+bc$

**With this we are clear that with $X1'$ we have to consider $a's$ input and with $X1$ we have to consider $b's$ input.**

**So, **

Output of $mux_{1}:$ $g=X1'.1+X1.0=X1'$

Output of $mux_{2}:$ $X2'g+X2.X1=X2'(X1')+X2.X1=$ $X1X2+X1'X2'$

**Correct Answer is (C)**

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