NAND gates can be used to form AND gate. What is the the minimum number of NAND gates required for this purpose?

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To determine the minimum number of NAND gates required to form an AND gate, we can follow these steps:

### Step 1: Understand the NAND Gate Functionality
The NAND gate outputs a low signal (0) only when all its inputs are high (1). In other words, the output of a NAND gate is the negation of the AND operation. Therefore, the truth table for a NAND gate is as follows:

| A | B | NAND (A, B) |
|---|---|-------------|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |

### Step 2: Define the AND Gate Functionality
The AND gate outputs a high signal (1) only when all its inputs are high (1). The truth table for an AND gate is:

| A | B | AND (A, B) |
|---|---|------------|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

### Step 3: Create the Configuration Using NAND Gates
To create an AND gate using NAND gates, we can use the property that the output of a NAND gate can be inverted by passing it through another NAND gate.

1. **First NAND Gate**: Connect inputs A and B to the first NAND gate. The output will be \( X = \overline{A \cdot B} \).
2. **Second NAND Gate**: Connect the output \( X \) from the first NAND gate to both inputs of the second NAND gate. The output will be \( Y = \overline{X \cdot X} = \overline{\overline{A \cdot B}} = A \cdot B \).

### Step 4: Conclusion
Thus, to form an AND gate using NAND gates, we need a minimum of **2 NAND gates**.

### Final Answer
The minimum number of NAND gates required to form an AND gate is **2**.

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