Boolean Algebra

A+B = A or B
A.B = A and B
de morgan's theorem

logic gates

AND gate: only outputs 1 if both inputs are 1.
NOT gate: changes 1 to 0 and 0 to 1.
OR gate : outputs 1 if has 1 as any input.
NAND gate: only outputs 0 if both inputs are 1.
NOR gate : only outputs 1 if both inputs are 0.
XOR gate :  only outputs 1 if the inputs are 1 and 0 pair.
XNOR gate : only outputs 1 if the inputs are the same.