Boolean Algebra

Boolean algebra is the category of algebra in which the variable’s values are the truth values, true and false ordinarily denoted 1 and 0 respectively. It is used to analyze and simplify digital circuits or digital gets.

Boolean Algebra Operations

  • Conjunction or AND 

A

B

A ∧ B

1

1

1

1

0

0

0

1

0

0

0

0
  • Disjunction or OR 

A

B

A V B

1

1

1

1

0

1

0

1

1

0

0

0
  • Negation or NOT 

A

ㄱA

1

0

0

1


Laws of Boolean Algebra

  • Commutative law
    • AB = BA
    • A+B = B+A
  • Associative law
    • (AB)C = A(BC)
    • (A+B) +C = A+(B+C)
  • Distributive law
    • A(B+C) = (AB) + (AC)
    • A+(BC) = (A+B) (A+C)
  • AND law
    • A0 = 0
    • A1 = A
    • AA = A
    • AA’ = 0
  • OR law
    • A + 0 = A
    • A + 1 = 1
    • A + A = A
    • A + A’ = 1
  • Inverse law
    • A + (A’)’ = 1


Logical Gates

  • AND
  • OR
  • NOT



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