Experiment 11 - The Distributive Law

The distributive law, often also called distributivity, states the behavior of the AND and OR operations on dissolving brackets.

Distributive Law (AND over OR)

The distributive law of an AND operation over an OR operation reads...

$$A \wedge (B \vee C) = (A \wedge B) \vee (A \wedge C)$$

     

Logic diagram distributive law of an AND operation over an OR operation.

     

Logic circuit distributive law of an AND operation over an OR operation I. (Enlarge)

     

Logic circuit distributive law of an AND operation over an OR operation II. (Enlarge)

Distributive Law (OR over AND)

The distributive law of an OR operation over an AND operation reads...

$$A \vee (B \wedge C) = (A \vee B) \wedge (A \vee C)$$

     

Logic diagram distributive law of an OR operation over an AND operation.

     

Logic circuit distributive law of an OR operation over an AND operation I. (Enlarge)

     

Logic circuit distributive law of an OR operation over an AND operation II. (Enlarge)

Comparison Arithmetic - Boolean algebra The distributive law for the basic arithmetic operations only applies to the multiplication over addition... $$x \times (y + z) = x \times y + x \times z$$