Question

To obtain the given truth table, the following logic gate should be placed at G

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

Hint:

For analyzing logic circuits: - Start by identifying the effect of NOT, AND, and OR gates on the inputs. - Derive the Boolean expression for the final output. - Compare the derived expression with standard logic gate outputs to determine the correct gate.

Answer 1

The Correct Option is C

Step 1: Examine the circuit configuration. The provided circuit features two NOT gates applied to inputs \( A \) and \( B \). Their outputs then connect to two AND gates, which subsequently feed into gate \( G \). The resulting truth table shows \( Y \) being high only when \( (A, B) \) is \( (0,0) \) or \( (1,1) \), and low for all other input combinations.

Step 2: Determine the logical expression. The observed output pattern directly matches the NOR operation, represented by the equation: \[ Y = \overline{A + B}. \]

Step 3: Choose the correct gate. The sole logic gate capable of implementing the expression \( Y = \overline{A + B} \) is the NOR Gate. 

- Therefore, gate \( G \) must be a NOR gate. The correct selection for gate \( G \) is a NOR gate. The final answer is \( \boxed{\text{NOR Gate}} \).