One important
concept in digital electronics design is known as
De
Morgan's Theorem.
This theorem basically states that:
1) the complement of the product of a given set of variables is equal to
the sum of the complements of the individual variables; and
2) the complement of the sum of a given set of variables is equal to the
product of the complements of the individual variables. De Morgan's
Theorem applies to any arbitrary number of variables.
The important
implication of De Morgan's Theorem is that any logic gate or circuit can
be replaced by an equivalent circuit composed of other gates, as long as
the NOT function can be provided by at least one of the substitute
gates. This is useful in digital electronics design wherein there is a
need to minimize the variety and number of logic gate IC's used.
Table 1 shows
the mathematical forms of De Morgan's Theorem.
Table 1. De Morgan's
Theorem
|
A · B
= A
+
B
A + B
=
A
·
B
A · B ·
C
····
= A + B
+
C + ···
A
+ B
+
C
+
···
=
A
· B
·
C
····
|
See Also:
Boolean
Algebra;
Logic Gates
