Boolean algebra
EE2315
What is Boolean algebra?
 It is a mathematical operation that works with the binary
numbers.
 Boolean algebra is used to analyze and simplify the
digital circuits.
 Boolean algebra and the Boolean operations are the
basis for computer logic.
Rules
 Variables used can have only two values either 1(True)
or 0 (false).
 Overbar represents a complement of a variable, where
the complement of A can be represented as 𝐴.
 A OR B  A+B
 A AND B  A.B
Boolean laws
Commutative law
A+B = B+A
A.B = B.A
Associative law
(A+B)+C = A+(B+C)
(A.B).C = A.(B.C)
Distributive law
A.(B+C) = A.B + A.C
Boolean laws
Annulment
𝐴. 0 = 0
𝐴 + 1 = 1
Identity law
𝐴 + 0 = 𝐴
 𝐴. 1 = 𝐴
Complement
𝐴 + 𝐴 = 1
 𝐴. 𝐴 = 0
Boolean laws
 Idempotent law
 𝐴. 𝐴 = 𝐴
𝐴 + 𝐴 = 𝐴
 Inversion law
𝐴 = 𝐴
 Absorption law
 𝐴 + 𝐴𝐵 = 𝐴
 𝐴. 𝐴 + 𝐵 = 𝐴
 𝐴 + 𝐴𝐵 = 𝐴 + 𝐵
 𝐴. 𝐴 + 𝐵 = 𝐴𝐵
DE Morgan's Theorem
 Compliment of a product is equal to the sum of the
compliments.
𝐴𝐵 = 𝐴 + 𝐵
 Compliment of a sum is equal to the product of the
compliments.
𝐴 + 𝐵 = 𝐴. 𝐵
Thank you.