Question

The boolean expression for output $Y$ of a system shown in the figure will be :

• A. $A.\overline{B}+\overline{A}.B$
• B. $(\overline{A}+\overline{B})(A+B)$
• C. $\overline{A}.\overline{B}+A.B$
• D. $A.B+(\overline{A}+\overline{B})$

Answer 1

The correct option is C $\overline{A}.\overline{B}+A.B$

The same conducting wire will carry the same input value to which it is connected.

The distribution of input values is shown in figure,


As, the final gate is an $\text{OR}$ gate,

$\Rightarrow Y=(\overline{A}.\overline{B})+(A.B)$

Hence, option $\left(C\right)$ is correct.