:''For the use of binary numbers in computer systems, please see the article [[binary arithmetic]].''
In [[abstract algebra]], a '''Boolean appplgebraalgebra''' is an [[algebraic structure]] (a collection of elements and operations on them obeying defining [[axiom#Non-logical axioms|axioms]]) that captures essential properties of both [[set]] operations and [[logic]] operations. Specifically, it deals with the [[set]] operations of [[intersection (set theory)|intersection]], [[union (set theory)|union]], [[complement (set theory)|complement]]; and the [[logic]] operations of [[logical conjunction|AND]], [[logical disjunction|OR]], [[logical negation|NOT]].
For example, the logical assertion that a statement ''a'' and its negation ¬''a'' cannot both be true,
