exclusive or
Sign in to saveAlso known as exclusive disjunction, XOR, EOR, EXOR, ⊻, ≢, ↮, disjoint
true when either but not both inputs are true
Key facts
- Truth table
- ( 0110 ) {\displaystyle (0110)}
- Disjunctive
- x ¯ ⋅ y + x ⋅ y ¯ {\displaystyle {\overline {x}}\cdot y+x\cdot {\overline {y}}}
- Conjunctive
- ( x ¯ + y ¯ ) ⋅ ( x + y ) {\displaystyle ({\overline {x}}+{\overline {y}})\cdot (x+y)}
- Zhegalkin polynomial
- x ⊕ y {\displaystyle x\oplus y}
- 0 preserving
- yes
- 1 preserving
- no
- Monotone
- no
- Affine
- yes
- Self dual
- no
via Wikipedia infobox
Wikidata facts
- Instance of
- logical operator
- Image
- Venn0110.svg
Show 5 more facts
- Stack Exchange tag
- stackoverflow.com/tags/xor
- TeX string
- \oplus
- Unicode character
- ⊻
- Commons category
- Exclusive disjunction
- maintained by WikiProject
- WikiProject Mathematics
Sources (2)
via Wikidata · CC0
~18 min read
Encyclopedic overview
Related concepts
Propositional calculus Predicate logic Boolean algebra Truth table Truth function Boolean function Functional completeness Scope (logic)
Excerpted from Wikipedia’s “exclusive or” article, available under the CC BY-SA 4.0 licence.