Universal Gates

NAND and NOR gates are called universal gates because you can combine them to produce all of the other gates. Non-inverting gates do not have this versatility because they cannot produce an inverted state.

NOT GATE

It is simple to make NAND and NOR gates into NOT gates. You just 'tie' the inputs - you make both inputs the one value.

AND GATE

OR GATE

NAND GATE from NOR and NOR GATE from NAND

XOR GATE