ECE 275 Boolean Algebra

AND Theorem

X * 0 = 0 X * 1 = X

OR Theorem

X + 0 = X X + 1 = 1

Idempotent Laws

X + X = X X * X = X

Laws of Complementarity

X + X' = 1 X * X' = 0

Elimination Theorem

X + X'Y = X + Y X(X' + Y) = XY

Absorption Theorem

X + XY = X X(X + Y) = X

Commutative Laws

X + Y = Y + X XY = YX

Distributive Laws

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

Consensus Theorem

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

Uniting Theorem

XY + XY' + X (X + Y)(X + Y') = X

Associative Law

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

DeMorgan Law

(X + Y)' = X'Y' (XY)' = X' + Y'

Involuntion Law

(X')' = X