# De Morgan's Laws ## First Law $\overline{A + B} = \overline{A} \cdot \overline{B}$ ## Second Law $\overline{A \cdot B} = \overline{A} + \overline{B}$ # Rules of Boolean Algebra ## Like Maths - $X \cdot 0 = 0$ - $X \cdot 1 = X$ - $X + 0 = X$ ### Commutative - $X \cdot Y = Y \cdot X$ - $X + Y = Y + X$ ### Associative - $X \cdot (Y \cdot Z) = (X \cdot Y) \cdot Z$ - $X + (Y + Z) = (X + Y) + Z$ ### Distributive - $X \cdot (Y + Z ) = X \cdot Y + X \cdot Z$ - $(X + Y) \cdot (W + Z ) = X \cdot W + X \cdot Z + Y \cdot W + Y \cdot Z$ ## Not Like Maths - $X \cdot X = X$ - $X \cdot \overline{X} = 0$ - $X + 1 = 1$ - $X + X = X$ - $X + \overline{X} = 1$ - $\overline{\overline{X}} = X$ ### Absorption - $X + ( X \cdot Y) = X$ - $X \cdot ( X + Y) = X$ # Interested in knowing more? - [Make a Calculator using only Marbles](https://youtu.be/i1e0T7lAELQ?si=vtpMcyT50FD1TmSo) -