Boolean Algebra

(A+0)//(A+A)=A=(A.1)//(A.A)
(A+1)//(A+A’)=1 (A.0)=0=(A.A’)

This Emplies,

Boolean Algebra – Key Points

1. Definition
   Mathematical system used in digital circuits.
   Variables have only two values: 0 (False) and 1 (True).

2. Basic Operations
   AND (·)
   1·1 = 1, otherwise 0

OR (+)
0+0 = 0, otherwise 1

NOT (')
0' = 1
1' = 0

3. 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

4. Commutative Law
   A + B = B + A
   A · B = B · A

5. Associative Law
   (A + B) + C = A + (B + C)
   (A · B) · C = A · (B · C)

6. Distributive Law
   A · (B + C) = AB + AC
   A + BC = (A + B)(A + C)

7. De Morgan’s Theorem
   (A + B)' = A'B'
   (AB)' = A' + B'

8. Absorption Law
   A + AB = A
   A(A + B) = A

9. Principle of Duality
   Replace + with · and 0 with 1 to get dual expression.

10. Boolean Functions
    Logical expressions made using variables and operators used to design digital circuits.