AIIMS 2006 Physics Logic Gates MCQ Question

To determine which logic operation the given circuit represents, we must first understand the characteristics of the basic logic gates: AND, NOT, OR, and NOR.

Explanation of the Correct Answer (A: AND)

An AND gate is a fundamental digital logic gate that outputs true (1) only when all its inputs are true (1). The truth table for an AND gate with two inputs $A$ and $B$ is as follows:

This means that the output is true only when both inputs $A$ and $B$ are true. Mathematically, this can be expressed as:

$$Y = A \cdot B$$

where $Y$ is the output, and $\cdot$ denotes the AND operation.

If the circuit in question shows a configuration where the output is high (1) only when both inputs are high (1), then it represents the AND operation.

Clarification of Incorrect Options

1. B) NOT:

   • A NOT gate, also known as an inverter, outputs the opposite value of its input. Its truth table is:

   A	Output (NOT A)
   0	1
   1	0

   For a NOT gate, the output is given by:

   $$Y = \overline{A}$$

   Therefore, if the circuit has more than one input or does not invert a single input, it cannot be a NOT gate.

2. C) OR:

   • An OR gate outputs true if at least one of its inputs is true. Its truth table is:

   A	B	Output (A OR B)
   0	0	0
   0	1	1
   1	0	1
   1	1	1

   Mathematically:

   $$Y = A + B$$

   If the circuit only outputs true when both inputs are true, it cannot be an OR gate.

3. D) NOR:

   • A NOR gate is the negation of an OR gate. It outputs true only when all inputs are false. Its truth table is:

   A	B	Output (A NOR B)
   0	0	1
   0	1	0
   1	0	0
   1	1	0

   The output can be expressed as:

   $$Y = \overline{(A + B)}$$

   Since the correct answer indicates that the output is true only when both inputs are true, the circuit cannot represent a NOR gate.

Conclusion

In conclusion, if the circuit indeed shows that it outputs a high signal only when both inputs are high (1), then the correct answer is A) AND. Other options are ruled out based on their definitions and truth tables, making the AND gate the only valid representation for the given circuit.