AND
1 AND 1 gives 1. Any other input gives 0.
NAND
(NOT AND) 1 AND 1 gives 0. Any other input gives 1.
OR
0 OR 0 gives 0. Any other input gives 1.
NOR
(NOT OR) 0 OR 0 gives 1. Any other input gives 0.
XOR
Equal inputs give 0. Non equal inputs give 1.
NOT
Invert input bits. 0 becomes 1. 1 becomes 0.