AIIMS 2007 Physics Logic Gates Assertion Reason Question

To address the question, let’s analyze both the assertion and the reason in detail.

Assertion: NAND is a universal gate.

The assertion that NAND is a universal gate is true. A universal gate is defined as a gate that can be used to construct any other type of logic gate (AND, OR, NOT, etc.) and, consequently, any digital logic circuit.

Reason: It can be used to describe all other logic gates.

The reason provided is also true. The NAND gate can indeed be combined in various configurations to create all other fundamental logic gates:

• NOT Gate: A single NAND gate can function as a NOT gate by connecting both its inputs to the same signal. For example, if the input is $A$, then the output will be $\overline{A}$ (the negation of $A$).

  $\text{NOT}(A) = A \text{ NAND } A = \overline{A}$

• AND Gate: To create an AND gate using NAND gates, you can use two NAND gates. The first NAND gate takes inputs $A$ and $B$ and outputs $\overline{A \cdot B}$. The second NAND gate takes this output and feeds it back into itself to invert it, yielding the AND function:

  $A \text{ AND } B = \overline{(A \text{ NAND } B)} = \overline{\overline{A \cdot B}}$

• OR Gate: Similarly, to construct an OR gate, you can use three NAND gates. By appropriately connecting them, you can achieve the OR function.

Thus, the reason correctly explains the assertion because it illustrates how the NAND gate can indeed be used to construct any other gate.

Conclusion on the Correct Answer

Since both the assertion and reason are true, and the reason correctly explains the assertion, the correct answer is:

A) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

Clarification of Incorrect Options

• B) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
  This option is incorrect because the reason does indeed explain why NAND is a universal gate.

• C) Assertion is true but Reason is false.
  This option is incorrect since both the assertion and the reason are true.

• D) Both Assertion and Reason are false.
  This option is incorrect because both statements are true.

Summary

In summary, both the assertion that NAND is a universal gate and the reason that it can be used to describe all other logic gates are correct. This demonstrates the versatility of the NAND gate in digital electronics, confirming that the correct answer is option A.