Shannon's switching circuits

Statement

Boolean algebra can be applied to the analysis and synthesis of relay and switching circuits. Shannon showed that any two-valued logic can be realized by networks of relays and switches—the foundation of digital circuit design. This thesis bridged symbolic logic and electrical engineering, enabling the design of computers and communication systems.

Formula

Boolean algebra → relay/switching circuits

Equation

AND = series, OR = parallel, NOT = normally closed

Proof sketch

Shannon's master's thesis "A Symbolic Analysis of Relay and Switching Circuits" (MIT, 1937) demonstrated that the algebra of logic (Boole, Huntington) directly applies to circuits: series connection implements AND, parallel implements OR, and normally closed contacts implement NOT. This established the theoretical basis for digital design.