Boolean Algebra

Basic identities used in boolean algebra digital logic.

Note that X' means not X, the complement of X

1. X+0 = X
2. X.1 = X
3. X+1= 1
4. X.0 = X
5. X+X = X
6. X.X=X
7. X+X'=1
8. X.X'=0
9. X''=X

Other boolean algebra properties.

• Commutative: X+Y = Y+X
• Associative: X+(Y+Z) = (X+Y)+Z
• Distributive: X(Y+Z) = XY + XZ
• DeMorgan's: (X+Y)' = X'+Y'

The identities below are useful for simpling the logic equations.

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

Boolean algebra digital logic tutorial.