XOR Gate
Output is 1 when inputs differ.
Formula
Variables
Example
1⊕1 = 0
How it works
An XOR gate compares two binary inputs and turns the output on only when the inputs are different. In digital logic, this is useful because it acts like a "mismatch detector": 0 and 1 produce 1, while 0 and 0 or 1 and 1 produce 0. The symbol \(\oplus\) is used because XOR is a standard logical operation in Boolean algebra and matches the idea of “exclusive or.”
When to use it
Use XOR when you need to detect inequality between two bits or toggle a state based on an input change. It appears in parity checking, adders in digital circuits, and simple control logic where only one of two signals should be active.
Worked example, step by step
Let A = 0 and B = 1 Y = A \oplus B Y = 0 \oplus 1 Y = 1 So, the output is 1 because the inputs are different.
Common mistakes to avoid
- Treating XOR like ordinary OR, where any 1 input would give 1
- Thinking XOR gives 1 when both inputs are 1
- Forgetting that XOR depends on the inputs being different, not just on the presence of a 1
Did You Know?
The XOR gate outputs true only when inputs differ, making it the heart of binary addition and simple encryption.
Share this formula
More in Electronics & Circuits
View allOhm's Law
BasicVoltage equals current times resistance.
Electrical Power (VI)
BasicPower dissipated by a component.
Power (I²R)
BasicPower lost as heat in a resistor.
Power (V²/R)
BasicPower from voltage and resistance.
Resistors in Series
BasicSeries resistances add directly.
Resistors in Parallel
IntermediateReciprocals of parallel resistances add.