How many NOR gates are used to form an AND gate

Options

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

Answer

To determine how many NOR gates are used to form an AND gate, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the NOR Gate**:
- A NOR gate is a digital logic gate that outputs true or high (1) only when both of its inputs are false or low (0). The output of a NOR gate can be expressed as:
\[ Y = \overline{A + B} \]
- This means the output Y is the negation of the logical OR of inputs A and B.

2. **Creating the Complement of Inputs**:
- To create an AND gate using NOR gates, we first need to obtain the complements of the inputs A and B.
- We can achieve this by connecting each input to a NOR gate.
- For input A:
- Connect A to both inputs of a NOR gate. The output will be:
\[ A' = \overline{A + A} = \overline{A} \]
- For input B:
- Connect B to both inputs of another NOR gate. The output will be:
\[ B' = \overline{B + B} = \overline{B} \]

3. **Combining the Outputs**:
- Now, we have the outputs A' and B' from the two NOR gates.
- To form an AND gate, we need to combine these outputs using another NOR gate:
- Connect A' and B' to the inputs of a third NOR gate. The output will be:
\[ Y = \overline{A' + B'} = \overline{\overline{A} + \overline{B}} \]

4. **Applying De Morgan's Theorem**:
- According to De Morgan's theorem:
\[ \overline{\overline{A} + \overline{B}} = A \cdot B \]
- Thus, the output Y from the third NOR gate is equivalent to the AND operation of inputs A and B.

5. **Counting the NOR Gates**:
- We used:
- 1 NOR gate to get A'
- 1 NOR gate to get B'
- 1 NOR gate to combine A' and B'
- Therefore, the total number of NOR gates used to form an AND gate is **3**.

### Final Answer:
**3 NOR gates are required to form an AND gate.**

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