Boolean Algebra

Boolean algebra is the original theoretical area dealing with only true and false. It's this area of mathematics that introduced AND, OR, XOR, NOT etc. concepts for boolean inputs.

This is the basis of bit-wise and binary-arithmetic fields.

Boolean to Binary Encoding

This a very important mental model to have. Binary and boolean aren't same. It's just that the binary is used to represent boolean values.

Standard Boolean Operators

Operator	Symbol	Description	Input causing output = True	Input causing output = False
NOT	¬, ~	Flips the value	Input = False	Input = True
AND	∧, ·	True only if both are true	Both True	Any False
OR	∨, +	True if at least one is true	Any True	Both False
XOR	⊕, ⊻	True if inputs are different	Inputs differ	Inputs same
NAND	↑, ⊼	Opposite of AND	Any False	Both True
NOR	↓, ⊽	Opposite of OR	Both False	Any True
XNOR	⊙, ≡	True if inputs are the same	Inputs same	Inputs differ

s