Boolean algebra is a branch of algebra used to analyze and simplify digital circuits.
The logic gates are the basic building blocks of digital systems. Each logic gate applies a specific logic to input variables to generate the output. The logic gates can have any number of input but only one output.
The truth table describes the function of a logic gate. Each logic gate is associated with a truth table. Kindly check this video for a simple description about the truth table.
Boolean Algebra Introduction: • Boolean Algebra | (Simple introduction)
Logic Gates: • Basic Logic Gates | AND | OR | NOT
A Boolean expression is a logical statement that can either be TRUE or FALSE.
Boolean expressions can take several forms and can have any number of variables.
The Boolean expressions are written following certain Boolean algebra rules.
Rule 1: The variables in Boolean algebra can have only two possible values: 0 (logical False) and 1 (logical True).
Rule 2: Logical AND of two or more variable is represented with a ‘.’ dot.
Rule 3: Logical OR of two or more variable is represented with a ‘+’ sign
Rule 4: Complement of a variable is represented by an overbar (⁻)
Laws of Boolean Algebra
The Boolean Laws are used to reduce and simplify a complex Boolean expression
Annulment Law: A.0 = 0 A + 1 = 1
Identity Law: A.1 = A A + 0 = A
Idempotent Law: A.A = A A + A = A
Complement Law: A. 𝐴 ̅ = 0 A + 𝐴 ̅ = 1
Commutative Law: A.B = B.A A + B = B + A
Distributive Law: A + (B.C) = (A + B).(A + C) A (B + C) = A.B + A.C
Associative Law: (A.B)C = A(B.C) (A + B) + C = A + (B + C)
Absorption Law: A (A + B) = A A + (A.B) = A
Double Negation Law: 𝐴 ̿ = A
De-Morgan’s Law: ( 𝐴.𝐵) ̅ = 𝐴 ̅ + 𝐵 ̅ (𝐴+𝐵) ̅ = 𝐴 ̅ . 𝐵 ̅
The laws of Boolean algebra are described with the corresponding logic gates and proved using their truth table. Watch this video till the end
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