Question

The Boolean expression for the given combination of logic gates is

• A. \(Y = (A+B)\cdot \overset{̄}{C}\)
• B. \(Y = (A\cdot B)\cdot \overset{̄}{C}\)
• C. \(Y = (A+B)+C\)
• D. \(Y = (A\cdot B)+\overset{̄}{C}\)

Hint:

Trace the signal through each gate: AND on A and B, NOT on C, then OR.

Answer 1

The Correct Option is D

Step 1: Read the circuit
The figure shows inputs A and B going into an AND gate. Input C goes into a NOT gate (triangle with a bubble). The outputs of the AND gate and the NOT gate then feed an OR gate, whose output is Y.

Step 2: Write each gate
AND output: \(A\cdot B\). NOT output: \(\overline{C}\).

Step 3: Combine in the OR gate
\[ Y = (A\cdot B) + \overline{C} \]

Step 4: Check the options
Option (A) and (B) have \(\overline{C}\) multiplied, which would be an AND, while the figure shows an OR. Option (C) lacks the NOT on C and has OR instead of AND on A and B. So the answer is option (D).

Final Answer:
The output is (A AND B) OR (NOT C). This is option (D). \[ \boxed{\text{(D) }Y=(A\cdot B)+\overline{C}} \]