The following truth table belongs to which one of the following four gates?
`|(A,B,C),(1,1,0),(1,0,0),(0,1,0),(0,0,1)|`

Options

A. OR
B. NAND
C. XOR
D. NOR

Answer

To determine which logic gate corresponds to the given truth table, we will analyze the outputs based on the inputs. The truth table provided is:

| A | B | C | Output |
|---|---|---|--------|
| 1 | 1 | 0 | ? |
| 1 | 0 | 0 | ? |
| 0 | 1 | 0 | ? |
| 0 | 0 | 1 | ? |

### Step-by-Step Solution:

1. **Identify the Inputs and Outputs**:
- The inputs are A, B, and C.
- We need to determine the output for each combination of inputs.

2. **Analyze the Output for Each Combination**:
- For the first row (A=1, B=1, C=0): The output is 0.
- For the second row (A=1, B=0, C=0): The output is 0.
- For the third row (A=0, B=1, C=0): The output is 0.
- For the fourth row (A=0, B=0, C=1): The output is 1.

3. **Compare with Logic Gates**:
- **AND Gate**: Outputs 1 only when all inputs are 1. (Does not match)
- **OR Gate**: Outputs 1 when at least one input is 1. (Does not match)
- **NAND Gate**: Outputs 0 only when all inputs are 1. (Does not match)
- **NOR Gate**: Outputs 1 only when all inputs are 0. (Matches with the last row)

4. **Confirm the NOR Gate**:
- The NOR gate outputs 0 for any input combination that includes at least one 1, and outputs 1 only when all inputs are 0.
- From the truth table, we see that the output is 0 for the first three combinations and 1 for the last combination, which confirms that this truth table corresponds to a NOR gate.

5. **Final Conclusion**:
- The truth table belongs to the NOR gate.