Question

The logic circuit shown above is equivalent to : 

• A. A
• B. B
• C. C
• D. D

Hint:

Use De Morgan's Law: $\overline{A \cdot B} = \overline{A} + \overline{B}$ and $\overline{A + B} = \overline{A} \cdot \overline{B}$ to simplify any complex logic circuit quickly.

Answer 1

The Correct Option is C

To determine the equivalent logic circuit, let's analyze the given circuit in the image.

The logic circuit in the question is composed of:

1. An OR gate with inputs A and B. The output will be A + B (logical OR operation).
2. A NOT gate (inverter) connected to the output of the OR gate. This will invert the output of the OR gate, producing \overline{A + B} (logical NOR operation).

Therefore, the logic expression for the circuit is \overline{A + B}, which is the NOR operation.

Now, let's examine the options:

1. Option A: It shows a NAND operation with inputs A and B. The output would be \overline{A \cdot B}, not matching our expression.
2. Option B: It shows an AND operation for an inverted A and B. This does not match our expression either.
3. Option C: It shows a NOR gate with inputs A and B, which results in \overline{A + B}. This matches our expression.
4. Option D: It involves another configuration that doesn't fit our expression.

Consequently, the correct logic circuit equivalent is represented by:

The correct answer is Option C, as it is a direct representation of the NOR operation.