Question

Identify the logic operation carried out by the given circuit : 

• A. AND
• B. OR
• C. NAND
• D. NOR

Hint:

Remember De Morgan's Law: $\overline{A+B} = \bar{A} \cdot \bar{B}$ and $\overline{A \cdot B} = \bar{A} + \bar{B}$. These are essential for simplifying complex logic gate diagrams.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A NAND gate with shorted inputs acts as a NOT gate. We can simplify the logical expressions for each stage of the circuit to determine the overall operation.
Step 2: Detailed Explanation:
1. The first part consists of two NAND gates where inputs are shorted.
For input \(A\), the output is \(X = \overline{A \cdot A} = \bar{A}\).
For input \(B\), the output is \(Y = \overline{B \cdot B} = \bar{B}\).
2. These outputs \(X\) and \(Y\) are fed into a NOR gate.
3. The final output \(Z\) is:
\[ Z = \overline{X + Y} \]
Substitute \(X = \bar{A}\) and \(Y = \bar{B}\):
\[ Z = \overline{\bar{A} + \bar{B}} \]
4. According to De Morgan's Law (\(\overline{P+Q} = \bar{P} \cdot \bar{Q}\)):
\[ Z = \bar{\bar{A}} \cdot \bar{\bar{B}} = A \cdot B \]
The expression \(Z = A \cdot B\) represents the AND operation.
Step 4: Final Answer:
The logical operation performed by the circuit is AND.