Question

The correct truth table for the given input data of the following logic gate is:

• A. A
• B. B
• C. C
• D. D

Hint:

Always simplify complex logic circuits by writing Boolean expressions and applying De Morgan’s laws to verify truth tables efficiently.

Answer 1

The Correct Option is D

Step 1: Identify individual logic operations.
From the given circuit:
Inputs \(A\) and \(B\) pass through an AND gate followed by a NOT gate (i.e., NAND operation).
Inputs \(C\) and \(D\) pass through an OR gate.
Outputs of these two branches are fed into an AND gate followed by a NOT gate (i.e., overall NAND).
Step 2: Write the Boolean expression.
The output \(Y\) can be written as: \[ Y = \overline{\left(\overline{A \cdot B} \cdot (C + D)\right)}. \] Using De Morgan’s theorem, \[ Y = (A \cdot B) + \overline{(C + D)}. \]
Step 3: Evaluate output for given input combinations.
Substituting the values of \(A, B, C, D\) row-wise, the output values match exactly with those shown in option (D).

Final Answer: \[ \boxed{\text{Option (D)}} \]