Linked from

The 80 pages that link to Boolean algebra, each with the reason it gives.

• Claude ShannonNarrower topic: Shannon showed that Boolean algebra describes the behavior of relay and switching circuits.

• Logic gateNarrower topic: Its operations define the functions that logic gates implement.

• Field-programmable gate arrayNarrower topic: FPGA logic implements Boolean functions using configurable hardware.

• Logical equivalenceNarrower topic: Its identities express propositional equivalences as algebraic rewrite laws.

• Digital logicNarrower topic: Its equations describe the logical behavior that digital circuits implement.

• Boolean functionNarrower topic: Its operations provide the standard language for expressing and manipulating Boolean functions.

• DisjunctionNarrower topic: Its operations provide an algebraic treatment of disjunction and its identities.

• NAND gateNarrower topic: NAND’s behavior can be expressed as the negation of a conjunction.

• UltrafilterNarrower topic: Subsets form a Boolean algebra, where ultrafilters choose one of each element-complement pair.

• Complementary metal–oxide–semiconductorNarrower topic: CMOS gate networks implement Boolean functions as transistor arrangements.

• OR gateNarrower topic: Its laws describe how OR gates combine and simplify within larger circuits.

• AND gateNarrower topic: Boolean algebra expresses the AND gate’s operation as multiplication-like conjunction.

• NOT gateNarrower topic: Boolean algebra expresses inversion as the complement operation, often written ¬A or A̅.

• XOR gateNarrower topic: Its identities describe how XOR combines with other logic operations.

• Hardware description languageNarrower topic: Combinational HDL expressions often implement Boolean functions.

• Karnaugh mapNarrower topic: Map groupings encode Boolean identities that eliminate variables from expressions.

• Arithmetic logic unitNarrower topic: Bitwise ALU operations implement Boolean functions independently across word bits.

• Electronic design automationNarrower topic: It supplies the logic that synthesis tools simplify and map into digital circuits.

• NOR gateNarrower topic: NOR is the negated OR operation within this algebra.

• Boolean prime ideal theoremNarrower topic: The theorem applies to every nontrivial structure of this kind.

• Synchronous circuitNarrower topic: Boolean functions specify the combinational logic between clocked state elements.

• Venn diagramNarrower topic: Its operations correspond to intersection, union, and complement in set diagrams.

• XNOR gateNarrower topic: XNOR behavior can be expressed and simplified with Boolean identities.

• Consensus theoremNarrower topic: The theorem is an identity within this algebra, using its operations and complement notation.

• Dynkin systemNarrower topic: Set algebras provide a broader algebraic perspective on complement and union operations.

• Binary multiplierNarrower topic: Gate-level multiplier designs implement arithmetic through Boolean functions.

• Boole's expansion theoremNarrower topic: Boole's theorem arose from this broader algebraic system.

• If and only ifNarrower topic: Its identities express biconditionals as equivalences between Boolean expressions.

• Stone's representation theorem for Boolean algebrasNarrower topic: Stone's result addresses the representation of this algebraic structure.