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parity has 6 distinct synonyms spread across 3 of its 5 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
(mathematics) a relation between a pair of integers: if both integers are odd or both are even they have the same parity; if one is odd and the other is even they have different parity
“parity is often used to check the integrity of transmitted data”
(computer science) a bit that is used in an error detection procedure in which a 0 or 1 is added to each group of bits so that it will have either an odd number of 1's or an even number of 1's; e.g., if the parity is odd then any group of bits that arrives with an even number of 1's must contain an error
(physics) parity is conserved in a universe in which the laws of physics are the same in a right-handed system of coordinates as in a left-handed system
Synonyms, antonyms and the broader and narrower relations for parity come from Princeton University’s WordNet. Full sources and licences.