Which of the following logic gates produces true only when one input is true and the other is false?
Explanation
1. The XOR Logic
The XOR gate follows the rule that the output is high (1) if and only if the inputs are unequal. If both inputs are the same (both 0 or both 1), the output is low (0).
2. Mathematical Representation
We can express the XOR operation using the symbol ⊕. For two inputs A and B, the output Y is defined by the following Boolean equation:
This can also be written in terms of basic gates (AND, OR, NOT) as:
3. Truth Table Verification
Let's look at the possible input combinations to see why it fits your description:
| Input A |
Input B |
Output Y |
Condition |
| 0 |
0 |
0 |
Same |
| 0 |
1 |
1 |
One True, One False |
| 1 |
0 |
1 |
One True, One False |
| 1 |
1 |
0 |
Same |
Conclusion
Since the output is 1 only for the cases (0,1) and (1,0), the XOR gate is the correct answer. In contrast, a standard OR gate would produce true even if both inputs were true.
