Experiment 15  The de Morgan Laws
The de Morgan laws formulated by Augustus de Morgan.
They consist of two statements
that describe the relationship between the negated AND and OR operations.
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...

