2.1 Boolean Algebra
Boolean algebra operates on the principle that any logical statement must be definitively either true or false; there are no intermediate states. A simple illustration of this is a light switch, which can only be either ON or OFF at any given moment, never both simultaneously.

Table 1 will then present the binary conditions and their alternative representations.

Table 1. Binary logic and other representation

Logic 1	Logic 0
True	False
High	Low
ON	OFF
YES	NO
Open	Close
+5v	0v

The fundamental rules governing Boolean algebra are called postulates. The most basic of these postulates deal with the TRUE or FALSE states of a single variable. Through logical deduction, examining all possible variations of a single variable (including its relation to itself, 1, and 0), we derive various equalities or identities. These identities are mathematical statements that are logically equivalent and thus interchangeable within a logic equation without changing the result. The standard mathematical equality symbol (=) is used in Boolean algebra to denote this equivalence.

The core postulates of Boolean algebra are derived from three basic logic functions: AND, OR, and COMPLEMENTATION. These postulates are expressed as algebraic equations using specific symbols for these functions.

Boolean algebra was first developed by George Boole in 1854 as a systematic approach to logic. Later, in 1938, C.E. Shannon adapted this concept into "switching algebra," a two-valued Boolean algebra used to model the behavior of bistable electrical switching circuits.