⚡ Logic Gate Truth Table Generator

Explore Digital Logic Gates and Boolean Algebra

Select Logic Gate

AND Gate
Output is TRUE only when all inputs are TRUE
Y = A · B

Truth Table

Gate Information

AND Gate

The AND gate outputs TRUE (1) only when all inputs are TRUE (1). If any input is FALSE (0), the output is FALSE.

Real-world analogy: Two switches in series - both must be closed for the light to turn on.

Boolean algebra: Y = A · B (or A AND B)

Applications:

  • Safety systems requiring multiple conditions
  • Masking operations in processors
  • Address decoders in memory circuits

Boolean Algebra Basics

Boolean algebra uses binary values (0 and 1) to represent FALSE and TRUE. Logic gates implement Boolean operations in hardware.

Gate Symbols

AND: D-shaped gate (multiplication)

OR: Shield-shaped gate (addition)

NOT: Triangle with circle (inversion)

NAND: AND gate with circle at output (universal gate)

NOR: OR gate with circle at output (universal gate)

XOR: Shield with extra line (exclusive OR)

XNOR: XOR with circle at output (equality)

Universal Gates

NAND and NOR gates are called "universal gates" because any Boolean function can be implemented using only NAND gates or only NOR gates.

De Morgan's Laws

Important identities in Boolean algebra:

NOT(A AND B) = (NOT A) OR (NOT B)
NOT(A OR B) = (NOT A) AND (NOT B)

These laws show the relationship between AND/OR gates and their negated forms (NAND/NOR).