To determine the minimum number of NOR gates required to create one NAND gate, we can follow these steps:
### Step-by-Step Solution:
1. **Understanding the NAND Gate**:
A NAND gate produces an output that is false only when all its inputs are true. The truth table for a NAND gate with two inputs (A and B) is as follows:
- A = 0, B = 0 → Output = 1
- A = 0, B = 1 → Output = 1
- A = 1, B = 0 → Output = 1
- A = 1, B = 1 → Output = 0
2. **Using NOR Gates**:
A NOR gate produces an output that is true only when all its inputs are false. The truth table for a NOR gate with two inputs (A and B) is:
- A = 0, B = 0 → Output = 1
- A = 0, B = 1 → Output = 0
- A = 1, B = 0 → Output = 0
- A = 1, B = 1 → Output = 0
3. **Constructing an AND Gate using NOR Gates**:
To create a NAND gate, we first need to create an AND gate using NOR gates. The AND gate can be constructed using the following logic:
- First, we need to invert the inputs A and B using NOR gates.
- We use two NOR gates to invert A and B:
- NOR1: Input A, Input A → Output A'
- NOR2: Input B, Input B → Output B'
- Now, we need to create an AND gate from these inverted inputs (A' and B'). This can be done using another NOR gate:
- NOR3: Input A', Input B' → Output = (A' NOR B') = (A AND B)'
4. **Creating the NAND Gate**:
Finally, to convert the AND gate into a NAND gate, we need one more NOR gate:
- NOR4: Input (A AND B)', Input (A AND B)' → Output = (A AND B)'' = A AND B
5. **Counting the Total NOR Gates**:
- 2 NOR gates for inverting A and B.
- 1 NOR gate to create the AND gate from the inverted inputs.
- 1 NOR gate to convert the AND output to NAND.
Therefore, the total number of NOR gates required is:
\[
2 + 1 + 1 = 4
\]
### Final Answer:
The minimum number of NOR gates required to make one NAND gate is **4**.
