Logic Gates

To determine the output in terms of inputs and , analyze the circuit step-by-step.

1. Inputs are and .
2. NOT gates produce: and .
3. First AND gate:
4. Second AND gate:
5. Outputs of both AND gates go to an OR gate.
6. Final output:

This is the standard expression of an XOR gate.

Final Answer:

To determine the correct Boolean operation represented by the given circuit diagram, we first need to analyze the behavior of the circuit with respect to the inputs A and B.

The circuit contains two switches labeled A and B. These switches act as inputs to the system, which can either be in the "on" position (represented as 1) or the "off" position (represented as 0). The LED will only light up based on the combined effect of these inputs.

Let's analyze the function of this circuit step by step:

1. If both inputs A = 1 and B = 1:
   • The circuit path is complete, allowing current to flow and lighting up the LED.
2. If either input A = 0 or B = 0:
   • The circuit path is broken, and current cannot flow, so the LED remains off.
3. If both inputs A = 0 and B = 0:
   • The circuit path is broken, and the LED remains off.

Now, compare this behavior to standard Boolean operations:

• The AND operation outputs 1 only when both inputs are 1.
• The OR operation outputs 1 if at least one input is 1.
• The NAND operation outputs 0 only when both inputs are 1 (opposite of AND).
• The NOR operation outputs 1 only when both inputs are 0 (opposite of OR).

Given the behavior of the circuit (LED only lights when the path is open by either switch off, i.e., A = 1 and B = 1 causes the LED to turn off), this represents a NAND operation. When both inputs are high, the output (LED) is off, which is characteristic of NAND.

Therefore, the correct Boolean operation represented by the circuit is: