For the logic gates shown below, the correct output is

For the logic gates shown below, the correct output is

1. $A+B+C$
2. $\bar{A} \cdot \bar{B} \cdot \bar{C}$
3. $\bar{A}+\bar{B}+\bar{C}$
4. $\overline{A \cdot B}+\overline{B \cdot C}$

Solution

For the logic gates shown below
The logic operation can be written as $ \begin{aligned} & \overline{A \cdot A}+(\overline{A \cdot B}+\overline{B \cdot C}+\overline{B \cdot B} \\ & =\overline{A \cdot A}+\bar{A}+\bar{B}+\bar{B}+C+\overline{B \cdot B} \quad(\text { Note } \overline{A \cdot A}=\bar{A}) \\ & =\bar{A}+\bar{A}+\bar{A}+\bar{B}+\bar{B}+\bar{C}+\bar{B} \quad(\text { Note } \bar{A}+\bar{A}=\bar{A}) \\ & =\bar{A}+\bar{B}+\bar{C} \end{aligned} $

Asked in: AP EAMCET 2022 (07 Jul Shift 2)

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