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Boolean Algebra
f-alpha.net » Mathematics » Algebra » Boolean Algebra » Let's go... » Experiment 15 - De Morgan Laws

Experiment 15 - The de Morgan Laws

First de Morgan Law

The de Morgan law of the negated AND operation reads...

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

Logic diagram de Morgan law of the negated AND operation.

Logic circuit de Morgan law of the negated AND operation I. (Enlarge)

Logic circuit de Morgan law of the negated AND operation II. (Enlarge)

Second de Morgan Law

The de Morgan law of the negated OR operation reads

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

     

Logic diagram de Morgan law of the negated OR operation.

Logic circuit de Morgan law of the negated OR operation I. (Enlarge)

Logic circuit de Morgan law of the negated OR operation II. (Enlarge)

The de Morgan laws have important applications. They are used in digital circuits to simplify logical problems and exchange logic gates against one another. More on this later...

Logic

The de Morgan laws were formulated in the 1850s in the context of the Boolean algebra. However, the logic was already known to the Greeks (Aristotle) over 2000 years ago...

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