Question

Identify the logic gate given in the circuit: 

 

• A. NAND gate
• B. OR gate
• C. AND gate
• D. NOR gate

Hint:

Applying De-Morgan’s theorem helps simplify logic expressions and identify equivalent gate functions in complex circuits.

Answer 1

The Correct Option is B

Step 1: {Understanding the Circuit} 
The circuit consists of NOT gates applied to \( A \) and \( B \), followed by an AND gate. 
Step 2: {Boolean Expression Derivation} 
\[ Y = \overline{\overline{A} \cdot \overline{B}} \] Applying De-Morgan's theorem: \[ Y = A + B \] 
Step 3: {Conclusion} 
The output matches the OR gate. Thus, the correct answer is (B). 
 

Answer 2

Step 1: Inversion
Each input is inverted: \[ A \rightarrow A', \quad B \rightarrow B' \]

Step 2: NAND Operation
The inverted values go into a NAND gate: \[ Y = \overline{A' \cdot B'} \]

Step 3: Apply De Morgan’s Theorem
Using De Morgan's Law: \[ Y = A + B \]

Final Result:
\[ \boxed{Y = A + B} \] Therefore, the logic gate implemented by the circuit is an OR gate.