Question

In the given logic circuit shown in the figure, inputs \( A \), \( B \), \( C \), and \( D \) are applied as shown. An LED is connected at the output. In which of the following combinations will the LED glow?

• A. \( A = 1 \), \( B = 1 \), \( C = 0 \), \( D = 0 \)
• B. \( A = 1 \), \( B = 0 \), \( C = 0 \), \( D = 0 \)
• C. \( A = 0 \), \( B = 1 \), \( C = 0 \), \( D = 0 \)
• D. \( A = 1 \), \( B = 1 \), \( C = 1 \), \( D = 1 \)

Hint:

To solve logic circuit problems, break down the circuit step by step and apply the appropriate truth tables for each gate.

Answer 1

The Correct Option is D

To determine when the LED glows in the given logic circuit, we need to analyze the inputs A, B, C, and D through the logic gates. The circuit involves AND and OR gates.

Let's analyze step by step:

1. Inputs A and B: They are inputs to an AND gate. The output of this gate will be 1 only if both A and B are 1.
2. Inputs C and D: They are inputs to another AND gate. The output of this gate will be 1 only if both C and D are 1.
3. OR Gate: The outputs of the two AND gates are inputs to an OR gate. The output of the OR gate will be 1 if any one of its inputs is 1, i.e., if either the output from the first AND gate or the second is 1.

The LED will glow if the output from the OR gate is 1. Let's check the combinations:

• \(A = 1\), \(B = 1\), \(C = 0\), \(D = 0\): The output from A and B's AND gate is 1, but C and D's gate is 0. OR gate gives 1, so LED glows.
• \(A = 1\), \(B = 0\), \(C = 0\), \(D = 0\): Neither AND gate gives 1, so OR gate is 0. LED does not glow.
• \(A = 0\), \(B = 1\), \(C = 0\), \(D = 0\): Neither AND gate gives 1, so OR gate is 0. LED does not glow.
• \(A = 1\), \(B = 1\), \(C = 1\), \(D = 1\): Both AND gates give 1, so OR gate gives 1. LED glows.

Therefore, the LED glows for the combination \(A = 1\), \(B = 1\), \(C = 1\), \(D = 1\).