Question

The truth table for the following logic circuit is:

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The correct option is D

Explanation for the correct answer:-

Option (D)

Step 1 Calculating the truth table for the following circuit,

From De Morgan's law we know,

$$\begin{gathered} \overline{A.B}=\overline{A}+\overline{B} \\ \overline{A+B}=\overline{A}.\overline{B} \end{gathered}$$

From both the laws, we can derive the equation from the figure,

$$\begin{gathered} y=\overline{\left(A\overline{B}+\overline{A}B\right)} \\ y=\overline{A\overline{B}}.\overline{\overline{A}B} \\ y=\left(\overline{A}+B\right).\left(\overline{B}+A\right) \end{gathered}$$

Using Distributive law,

$$\begin{gathered} y=\overline{A.}A+\overline{A}.\overline{B}+A.B+B\overline{B} \\ y=A.B+\overline{A}.\overline{B} \end{gathered}$$ Since, $$\begin{gathered} \overline{A.}A=0 \\ \overline{B}B=0 \end{gathered}$$

A	B	$y=A.B+\overline{A}.\overline{B}$
0	0	1
0	1	0
1	0	0
1	1	1

Hence option D is the correct option.