could any one please help in galois field

is primitive in GF(2)[x].

Let be a root of .

Addition:

α2 means 0 1 0 0

α5 means 0 1 1 1

- ----------------

when we add the both 1 0 1 1

but in galois field answer is α3 means that 0 0 1 1 from the table

please explain how it is

Multiplication:

in multiplication when we multiply two 4 bit numbers we got 8 bit number

in galois field we got 4 bit number only

please explain these two questions