NAND gate is-

Options

A. a basic gate
B. not a universal gate
C. a universal gate
D. a universal gate

Answer

### Step-by-Step Solution:

1. **Definition of NAND Gate**:
The NAND gate is a digital logic gate that outputs false only when all its inputs are true. It is the inverse of the AND gate.

2. **Truth Table of NAND Gate**:
The truth table for a NAND gate with two inputs (A and B) is as follows:
- When A = 0, B = 0 → Output = 1
- When A = 0, B = 1 → Output = 1
- When A = 1, B = 0 → Output = 1
- When A = 1, B = 1 → Output = 0
Thus, the output can be summarized as:
```
A | B | Output
0 | 0 | 1
0 | 1 | 1
1 | 0 | 1
1 | 1 | 0
```

3. **Why is it called a Universal Gate?**:
The NAND gate is termed a universal gate because it can be used to create any other type of logic gate, including AND, OR, and NOT gates.

4. **Implementation of AND Gate using NAND Gates**:
- To create an AND gate using NAND gates, connect the outputs of a NAND gate back to its inputs.
- For inputs A and B, the output of the first NAND gate is \( \overline{A \cdot B} \).
- If we take this output and feed it into another NAND gate (with both inputs being the output of the first NAND gate), we get:
\[ \text{Output} = \overline{\overline{A \cdot B}} = A \cdot B \]
Thus, we have constructed an AND gate.

5. **Implementation of OR Gate using NAND Gates**:
- To create an OR gate, first, invert both inputs using NAND gates.
- Connect inputs A and B to two separate NAND gates to get \( \overline{A} \) and \( \overline{B} \).
- Then, connect these outputs to another NAND gate:
\[ \text{Output} = \overline{\overline{A} \cdot \overline{B}} = A + B \]
Thus, we have constructed an OR gate.

6. **Implementation of NOT Gate using NAND Gates**:
- To create a NOT gate, connect the input A to both inputs of a NAND gate:
\[ \text{Output} = \overline{A \cdot A} = \overline{A} \]
Thus, we have constructed a NOT gate.

7. **Conclusion**:
Since the NAND gate can be used to construct NOT, AND, and OR gates, it is classified as a universal gate.

### Final Answer:
The NAND gate is a universal gate because it can be used to implement NOT, AND, and OR gates.

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