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Clarke and Monzo defined a construction called a generalized inflation of a semigroup, and proved that for unions of groups, all null extensions are generalized inflations. We characterize when a groupoid containing a completely simple semigroup B is an astsociative generalized inflation of B, and thus provide a way to construct all associative generalized inflations (null extensions) of a given completely simple semigroup.This answers a question posed by Clarke and Monzo.