Boolean Algebra is a form of algebra for manipulating boolean expressions. Unlike "normal" algebra, variables in boolean algebra are either True or False. (usually represented by 1 and 0.)

The basic boolean functions are AND, OR, and NOT.

AND is like multiplication in "normal" algebra.

OR is treated as addition.

NOT is represented by an apostrophe following the variable or expression.

__Some Basic Boolean Algebra:__

0' = 1 (*the inverse of 0 is 1*)

1' = 0 (*the inverse of 1 is 0*)

**Operations with 0 and 1:**

X + 1 = 1 (*X or 1/true = 1/true*)

X + 0 = X

X * 0 = 0 (*X and 0 = 0*)

X * 1 = X

**Idempotent laws:**

X + X = X

X * X = X

**Laws of complementarity:**

X + X' = 1

X * X' = 0

**Commutative Laws:**

X + Y = Y + X

XY = YX (*X and Y = Y and X*)

**Associative laws:**

(X + Y) + Z = X + (Y + Z) = X + Y + Z

(XY)Z = X(YZ) = XYZ

**Distributive laws:**

X(Y+Z) = XY + XZ

X + YZ = (X + Y)(X + Z)

From these basics others can easily be derived.