Digital Logic Suite

Boolean Algebra Solver

Test logic circuits and simplify boolean expressions instantly. Master the fundamentals of digital logic and computer science.

Boolean Logic Solver

Input A

Input B

AND (A ∧ B)0

OR (A ∨ B)1

XOR (A ⊕ B)1

NOT A (¬A)0

NAND1

NOR0

NOT B1

Truth Table Hint

AND is only true if both are true. OR is true if at least one is true. XOR is true if exactly one is true (they must be different). NAND and NOR are the inverted versions of AND and OR.

Logic Gate Guide

AND (Conjunction)

Output is 1 (True) only if both inputs are 1. Symbol: ∧ or ⋅

OR (Disjunction)

Output is 1 if at least one input is 1. Symbol: ∨ or +

NOT (Negation)

Inverts the input (0 becomes 1, 1 becomes 0). Symbol: ¬ or '

Why it Matters

"Boolean algebra is the foundation of all modern computing. Every decision a computer makes is ultimately reduced to a series of 0s and 1s processed through these basic logic gates."

Laws of Boolean Algebra

Commutative: A + B = B + A
Associative: (A + B) + C = A + (B + C)
Distributive: A(B + C) = AB + AC
De Morgan's: ¬(A ∧ B) = ¬A ∨ ¬B