Question

Output of following logic circuit is

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

Hint:

In logic circuits, OR gates correspond to addition \((+)\), AND gates correspond to multiplication, and NOT gates correspond to complement \((\overline{\phantom{A}})\).

Answer 1

The Correct Option is C

Step 1: Identify the gates in the circuit.
The circuit contains three OR gates whose outputs are connected to a final AND gate.
Hence, the final output will be the product of the outputs of the three OR gates.

Step 2: Determine the output of the first OR gate.
In the first gate, input \(A\) passes through a NOT gate. Therefore, it becomes \(\overline{A}\). The other input is \(B\).
Thus, output of first OR gate is
\[ \overline{A}+B \]

Step 3: Determine the output of the second OR gate.
In the second gate, inputs are \(\overline{A}\) and \(\overline{C}\).
Therefore, output of second OR gate is
\[ \overline{A}+\overline{C} \]

Step 4: Determine the output of the third OR gate.
In the third gate, inputs are \(B\) and \(\overline{C}\).
Hence, output of third OR gate is
\[ B+\overline{C} \]

Step 5: Write the final output.
The outputs of all three OR gates are connected to an AND gate. Therefore, overall output is
\[ (\overline{A}+B)(\overline{A}+\overline{C})(B+\overline{C}) \]

Step 6: Final conclusion.
Hence, the correct output expression is
\[ \boxed{(\overline{A}+B)(\overline{A}+\overline{C})(B+\overline{C})} \]