Boolean Algebra
The most obvious way to simplify Boolean expressions is to manipulate them in the same way as normal algebraic expressions are manipulated. With regards to logic relations in digital forms, a set of rules for symbolic manipulation is needed in order to solve for the unknowns.
A set of rules
formulated by the English mathematician George Boole describe certain
propositions whose outcome would be either true or false. With regard to
digital logic, these rules are used to describe circuits whose state can be either,
1 (true) or 0 (false). In order to fully understand this, the relation between
the AND gate, OR gate and NOT gate operations should be appreciated.
AND
Form
|
OR
Form
|
|
Identity
Law
|
A
● 1 = A
|
A
+ 1 = A
|
Zero
and one Law
|
A
● 0 = 0
|
A
+ 0 = 1
|
Inverse
Law
|
A
● A’ = 0
|
A
+ A’ = 1
|
Idempotent
Law
|
A
● A = A
|
A
+ A = A
|
Commutative
Law
|
A
● B = B ● A
|
A
+ B = B + A
|
Associate
Law
|
A
● (B ● C) = (A ● B) ● C
|
A
+ (B + C) = (A + B) + C
|
Distributive
Law
|
A
+ (B ● C) = (A + B) ● (A + C)
|
A
● (B + C) = (A ● B) + (A ● C)
|
Absorption
Law
|
A
(A + B) = A
|
A
+ A ● B = A
A
+ A’B = A + B
|
DeMorgan’s
Law
|
(A’
● B’) = A’ + B’
|
(A’
+ B’) = A’ ● B’
|
Double
Complement Law
|
X’’ = X
| |
De Morgan’s Law
Tips: Break the line, change the sign
De Morgan’s Law Logic Gates
by: Muhammad Nasruddin Rosli
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