Question

The output of the circuit is

• A. $\left(x_2+x_3\right)·\left[\left(x_1·x_2\right)·x_3^{\text{'}}\right]$
• B. $\left(x_2+x_3^{\text{'}}\right)+\left[\left(x_1·x_2\right)·x_3^{\text{'}}\right]$
• C. $\left(x_2+x_3\right)+\left[\left(x_1·x_2\right)·x_3^{\text{'}}\right]$
• D. $\left(x_1+x_3\right)+\left[\left(x_1·x_2\right)·x_3^{\text{'}}\right]$

Answer 1

The correct option is A

$\left(x_2+x_3\right)·\left[\left(x_1·x_2\right)·x_3^{\text{'}}\right]$

Step 1: Given the figure

Step 2: Pass $x_1,x_2$ to AND gate and $x_3$ to NOT gate

1. When the $x_1,x_2$ passed through AND gate produces the output $x_1·x_2$ and when $x_3$ passes through $NOT$ , it produces the output $x_3^{\text{'}}$.
2. When the obtained output $\left(x_1{x}_2\right)$ and $x_3^{\text{'}}$ passed through AND gate, it produces the output $x_1·x_2·x_3^{\text{'}}$.
3. The following figures represent this process
4. 

Step 3: Determine the circuit output

1. When the $x_2,x_3$ passed through the OR gate, it produces the $\left(x_2+x_3\right)$ .
2. Now the output of the previous step $x_1·x_2·x_3^{\text{'}}$ and $\left(x_2+x_3\right)$ passed through the AND gate that produces the circuit output $\left(x_2+x_3\right)·\left[x_1·x_2·x_3^{\text{'}}\right]$.

Hence, option (A) is the correct answer.