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An XOR gate (Exclusive OR gate) is a digital logic gate that outputs true (1) when the number of true inputs is odd. It implements the exclusive OR operation from mathematical logic, meaning it outputs true if one, and only one, of the inputs is true. If both inputs are false (0) or both are true, the output is false (0) 1.
Truth Table and Boolean Expression
The XOR gate can be represented by the following truth table:
| A | B | A XOR B | |---|---|---------| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 |
The Boolean expression for an XOR gate with inputs A and B is: [ X = A'B + AB' ] This means the output is true when A is true and B is false, or A is false and B is true 2.
Implementation
XOR gates can be implemented using various methods, including:
Transistor-based circuits: Using NPN transistors to create the XOR logic.
NAND gates: By combining NAND gates, we can achieve the XOR function.
NOR gates: Similarly, XOR can be implemented using NOR gates 2.
Applications
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