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: Read the circuit layout.
Three OR gates feed their outputs into one final AND gate, so the overall output is the product of the three OR outputs.
Step 2: First OR gate.
Its inputs are $\overline{A}$ (because $A$ passes through a NOT gate) and $B$, giving output \[ \overline{A} + B. \]
Step 3: Second OR gate.
Its inputs are $\overline{A}$ and $\overline{C}$, giving output \[ \overline{A} + \overline{C}. \]
Step 4: Third OR gate.
Its inputs are $B$ and $\overline{C}$, giving output \[ B + \overline{C}. \]
Step 5: Combine in the AND gate.
The AND of the three outputs is their product: \[ (\overline{A}+B)(\overline{A}+\overline{C})(B+\overline{C}). \]
Step 6: Conclude.
So the circuit output is the product of the three OR terms.
\[ \boxed{(\overline{A}+B)(\overline{A}+\overline{C})(B+\overline{C})} \]