Trying to understand simple bit states

I am trying to understand bits, operations and masking. I have a hard time to get this thing into my head. I have tried to read at many different websites without luck.

I have 8 states, going from 1 to 8:

state 1 = 0001
state 2 = 0010
state 3 = 0011
state 4 = 0100
state 5 = 0101
state 6 = 0110
state 7 = 0111
state 8 = 1000


Now I want to get state 1, 3, 6 and 8. I am unsure how to set this state in the bits. Either I can do this:

state 1 = 0001
state 3 = 0011
state 6 = 0110
state 8 = 1000


Which would turn out like this:

combinedStates = 1111


The problem is, if I send in this, state 5 will get triggered as well as:

state 1 = 0001
state 3 = 0011
state 5 = 0101
state 6 = 0110
state 8 = 1000


Because both state 5 and 6 has a 1 in the same place. The second thing would be to add all the state numbers together (1, 3, 6 and 8, which is 18):

combinedStates = 0001 0010 (18)


But then looking at state 6 would not work as:

state 6 = 0110
combinedStates = 0001 0010


There will be a missing 1.

How would I proceed if I want to get states 1, 3, 6 and 8: combine their bits, or add them all together and use that one's bit value? Any other approach? Any operand I should use?

Then you can just bitwise or (or add) them together. Many programming languages have a datastructure for "bitsets" that can help with this, especially if you have more bits than fit in a simple integer. Your example with just 8 states fits in a typical int, so you don't really need such a data structure.