The logic behind 'NOR' gate is that it gives

Options

A. high output when both inputs are high
B. high output when both inputs are low
C. low output when both inputs are low
D. none of these

Answer

To understand the logic behind a NOR gate, we can break down the problem step by step:

### Step 1: Understand the Inputs and Outputs
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).

### Step 2: Define the Inputs
Let's denote the inputs of the NOR gate as:
- Input A
- Input B

### Step 3: Write the Output Expression
The output (X) of a NOR gate can be expressed in Boolean algebra as:
\[ X = (A + B)' \]
This means that the output is the negation (NOT) of the logical OR of the inputs A and B.

### Step 4: Create a Truth Table
To visualize how the NOR gate operates, we can create a truth table:

| A | B | A + B | X = (A + B)' |
|---|---|-------|--------------|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 |

### Step 5: Analyze the Truth Table
From the truth table, we can see:
- When both inputs A and B are 0 (low), the output X is 1 (high).
- In all other cases (when at least one input is 1), the output X is 0 (low).

### Step 6: Conclusion
Therefore, the logic behind the NOR gate is that it gives a high output (1) only when both inputs are low (0).

### Final Answer
The correct option is that the NOR gate gives a high output when both inputs are low.

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