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Boolean algebra concerns representing values with
letters
and
simplifying
expressions
Boolean values
TRUE
and
FALSE
, which can be represented as 1 and 0 respectively
Boolean algebra notation
A,
B
, C, etc. (unknown
Boolean
values)
A
(NOT
A
)
A •
B
(A AND
B
)
AB
(alternative notation for A AND
B
)
A +
B
(A OR
B
)
Algebraic operations have an order of
precedence
, meaning that some operations must be applied
before
others
Order of precedence in Boolean algebra
Brackets
NOT
AND
OR
Boolean identities
A • 0 =
0
B
• 1 =
B
C •
C
=
C
D + 0 =
D
E +
1
=
1
F +
F
=
F
G =
G
De
Morgan's laws
"
Break the bar and change the sign
"
Applying De
Morgan's
laws
1.
Break
the
bar
2.
Change
the
sign
Distributive rules in Boolean algebra: A
•
(B + C) = A
•
B + A • C
Example 1: Simplify A + B • A
A
+
B
• A
=
B
+
A
=
1
Example 2: Simplify C • B + C • B
C •
B
+ C • B
=
B
• (
C
+ C)
=
B
