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Boolean Algebra
f-alpha.net » Mathematics » Algebra » Boolean Algebra » Let's go... » Experiment 11 - Distributive Law

Experiment 11 - The Distributive Law

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...

$$x \times (y + z) = x \times y + x \times z$$

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