The minimum NOR gates are required to make one NAND gate are

Options

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

Answer

To determine the minimum number of NOR gates required to create one NAND gate, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Function of a NAND Gate**:
- A NAND gate produces an output that is false only when all its inputs are true. The output can be expressed as \( Y = \overline{A \cdot B} \), where \( A \) and \( B \) are the inputs.

2. **Create a NOT Gate using NOR Gates**:
- A NOR gate can be configured to act as a NOT gate by connecting both inputs of the NOR gate to the same input signal.
- For example, if we input \( A \) into both inputs of a NOR gate, the output will be \( \overline{A} \).

3. **Construct the NAND Gate**:
- To create a NAND gate, we need to first create the AND operation and then negate it.
- We can create the AND operation using NOR gates by first creating NOT gates for each input.

4. **Create NOT Gates for Each Input**:
- Use two NOR gates to create NOT gates:
- First NOR gate: Input \( A \) to both inputs → Output: \( \overline{A} \)
- Second NOR gate: Input \( B \) to both inputs → Output: \( \overline{B} \)

5. **Combine the Outputs using a NOR Gate**:
- Now, take the outputs \( \overline{A} \) and \( \overline{B} \) and input them into another NOR gate:
- This NOR gate will output \( \overline{\overline{A} + \overline{B}} \).
- According to De Morgan's theorem, this simplifies to \( A \cdot B \).

6. **Negate the AND Output**:
- Finally, we need to negate the output of the AND operation to achieve the NAND operation:
- Use one more NOR gate with both inputs connected to the output of the previous NOR gate (which is \( A \cdot B \)).
- This will give us the final output \( \overline{A \cdot B} \), which is the NAND operation.

### Summary of Gates Used:
- 2 NOR gates to create NOT gates for \( A \) and \( B \).
- 1 NOR gate to create the AND operation from the outputs of the NOT gates.
- 1 NOR gate to negate the AND output.

### Total NOR Gates Required:
- Total = 2 (for NOT gates) + 1 (for AND) + 1 (for final NOT) = **4 NOR gates**.

### Final Answer:
The minimum number of NOR gates required to make one NAND gate is **4**.

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