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Monday, March 9, 2026
Boolean Algebra
(A+0)//(A+A)=A=(A.1)//(A.A)
(A+1)//(A+A’)=1 (A.0)=0=(A.A’)
Boolean Algebra – Key Points
-
Definition
Mathematical system used in digital circuits.
Variables have only two values: 0 (False) and 1 (True). -
Basic Operations
AND (·)
1·1 = 1, otherwise 0
OR (+)
0+0 = 0, otherwise 1
NOT (')
0' = 1
1' = 0
-
Basic Laws
Identity Law
A + 0 = A
A · 1 = A
Null Law
A + 1 = 1
A · 0 = 0
Idempotent Law
A + A = A
A · A = A
Complement Law
A + A' = 1
A · A' = 0
Double Negation
(A')' = A
-
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) = AB + AC
A + BC = (A + B)(A + C) -
De Morgan’s Theorem
(A + B)' = A'B'
(AB)' = A' + B' -
Absorption Law
A + AB = A
A(A + B) = A -
Principle of Duality
Replace + with · and 0 with 1 to get dual expression. -
Boolean Functions
Logical expressions made using variables and operators used to design digital circuits.