Question

The Universal gate is:

• A. AND
• B. OR
• C. NAND
• D. XOR

Hint:

Only NAND and NOR are classified as universal gates.
Using only NAND gates, the sequence of gate requirements for NOT, AND, OR, and XOR is 1, 2, 3, and 4 gates respectively.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks to identify the gate that is considered a "Universal gate" from the given options.
In digital electronics, a universal gate is one that can implement any Boolean function without requiring any other type of gate.

Step 2: Key Formula or Approach:
The basic logic gates (AND, OR, NOT) are sufficient to realize any digital circuit.
However, if a single gate type can reproduce the functionalities of all these three basic gates, it is classified as a universal gate.
The two universal gates in digital electronics are NAND and NOR gates.

Step 3: Detailed Explanation:
Let us analyze why NAND is a universal gate by deriving the basic gates from it:

• NOT Gate implementation: A NOT gate is realized by tying both inputs of a 2-input NAND gate together:
\[ Y = \overline{A \cdot A} = \overline{A} \]
• AND Gate implementation: An AND gate is realized by following a NAND gate with a NAND-gate inverter:
\[ Y = \overline{\overline{A \cdot B}} = A \cdot B \]
• OR Gate implementation: An OR gate is realized by inverting the inputs first using NAND inverters and then passing them through another NAND gate:
\[ Y = \overline{\overline{A} \cdot \overline{B}} = \overline{\overline{A}} + \overline{\overline{B}} = A + B \] Comparing this with the other options:
- AND (Option A) and OR (Option B) are basic logic gates and cannot implement other logical operations on their own.
- XOR (Option D) is an exclusive gate used for parity and arithmetic, but it is not universal.

Step 4: Final Answer:
The Universal gate among the options provided is the NAND gate.