Question

The correct Boolean operation represented by the circuit diagram drawn is :

• A. AND
• B. OR
• C. NAND
• D. NOR

Answer 1

The Correct Option is C

The question involves identifying the Boolean operation represented by the given circuit diagram. The circuit is essentially an arrangement of switches and resistors that influences the LED's state based on the logic operation performed.

Understanding the Circuit:

1. The circuit includes two switches, A and B, which can be either open (0 state) or closed (1 state).
2. The LED will light up only if a specific logical condition is met that corresponds to the logic gates created by the switches and the resistors.

Logic Analysis:

• If both switches A and B are closed (1 state), the path for current flow gets completed, making the LED light up. In typical logic gate scenarios, this outcome is characteristic of a NAND gate being "off" or "0" when both inputs are "1".
• If either A or B is open (0 state), the circuit breaks the path, and the LED will remain off. This matches the NAND operation where the output is "1" if any input is "0".
• If both inputs A and B are "0", the current path remains open, keeping the LED off, which is consistent with a "1" output in NAND logic (i.e., an inactive LED).

Conclusion:

The described behavior aligns with the properties of a NAND gate, wherein the output is false (0) only if all inputs are true (1).

• AND: The circuit description does not lead to simultaneous satisfaction of both input signals enabling output actively.
• OR: An OR gate will light the LED if either input is "1", which is not the case here.
• NOR: A NOR gate provides a true output only when both inputs are false (0), contrary to the described operation.
• NAND: As analyzed, the output is consistent only when both inputs are true, matching the false LED state. Therefore, the correct Boolean operation represented by this circuit is NAND.

Thus, the correct answer is: NAND