An exclusive-OR (XOR) gate is a digital logic gate that produces a true output (1) when exactly one of its inputs is true, and a false output (0) when both inputs are true or both inputs are false.
Truth Table
The following table shows the truth table for an XOR gate:
| Input 1 | Input 2 | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Symbol
The following is the symbol for an XOR gate:
Boolean Expression
The Boolean expression for an XOR gate is as follows:
A ⊕ B = (A + B) ⋅ (A' + B')
where:
- A and B are the inputs to the XOR gate
- A’ and B’ are the complements of A and B, respectively
- The symbol ⊕ represents the XOR operation
Applications
XOR gates are used in a variety of digital circuits, including:
- Adders and subtractors
- Comparators
- Parity generators and checkers
- Encoders and decoders
XNOR Gate
An exclusive-NOR (XNOR) gate is a digital logic gate that produces a true output (1) when both of its inputs are true or both of its inputs are false, and a false output (0) when exactly one of its inputs is true.
Truth Table
The following table shows the truth table for an XNOR gate:
| Input 1 | Input 2 | Output |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Symbol
The following is the symbol for an XNOR gate:
Boolean Expression
The Boolean expression for an XNOR gate is as follows:
A ≢ B = (A + B)'
where:
- A and B are the inputs to the XNOR gate
- The symbol ≢ represents the XNOR operation
Applications
XNOR gates are used in a variety of digital circuits, including:
- Parity generators and checkers
- Encoders and decoders
- Code converters
- Arithmetic circuits
Example
One common example of the use of XOR and XNOR gates is in parity generators and checkers. Parity generators are used to add a parity bit to a digital signal to detect errors. Parity checkers are used to check the parity bit of a digital signal to detect errors.
The following is a diagram of a parity generator circuit:
The parity generator circuit has three inputs, A, B, and C, and one output, Parity. The Parity output is a 1 if the number of 1s in the inputs is even, and a 0 if the number of 1s in the inputs is odd.
The XOR gates in the parity generator circuit are used to calculate the Parity output. The Parity output is equal to a 1 if any of the inputs are equal to 1, and 0 otherwise.