Question

Identify the logic operation carried out. 

• A. AND
• B. NAND
• C. NOR
• D. OR

Hint:

NAND gate with shorted inputs = NOT.
NOR gate with shorted inputs = NOT.
A NOR gate with NOT-ed inputs acts as an AND gate (Bubbled NOR = AND).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A NAND gate with its inputs tied together acts as a NOT gate.
A NOR gate with inputs \(X\) and \(Y\) produces the output \(\overline{X + Y}\).
Step 2: Key Formula or Approach:
Use Boolean algebra and De Morgan's Laws:
1. \(\text{NAND}(A, A) = \bar{A}\).
2. \(\text{NOR}(X, Y) = \overline{X + Y}\).
3. \(\overline{\bar{A} + \bar{B}} = A \cdot B\).
Step 3: Detailed Explanation:
Input \(A\) passes through a NAND gate with shorted inputs. The output is \(X = \bar{A}\).
Input \(B\) passes through a NAND gate with shorted inputs. The output is \(Y = \bar{B}\).
Both \(X\) and \(Y\) are then fed into a NOR gate.
The final output \(Y_{\text{out}}\) is:
\[ Y_{\text{out}} = \overline{X + Y} = \overline{\bar{A} + \bar{B}} \]
Applying De Morgan's Law (\(\overline{P + Q} = \bar{P} \cdot \bar{Q}\)):
\[ Y_{\text{out}} = \overline{(\bar{A})} \cdot \overline{(\bar{B})} = A \cdot B \]
The logical expression \(A \cdot B\) corresponds to the AND operation.
Step 4: Final Answer:
The logic operation is AND.