combining binary numbers

I'm working on a simple PHP permissions function at the moment. Users belong to any number of groups, and those groups have a binary number (saved in base 10) that represents whether they have access to one aspect of the site. It's a common method, but let me give an example just to clarify.

I want to find out if the current user has access to something with permission level of 8... 1000. He belongs to a group that has a permission level of 27... 11011. Thus, he has permission to view the content.

Now, a user can belong to multiple groups. I am looking for an easy method (hopefully a formula) to combine the permission levels of two groups. Say a user belongs to a group with a perm level of 25 (11001) and one of 3 (11). I want 27 spit out (11011).

I've been searching around, but I don't know exactly what to call this. Any help would be appreciated.

5 (101) + 1 (001) = 5 (101)
6 (110) + 5 (101) = 7 (111)
3 (011) + 2 (010) = 3 (011)

Thanks a lot.

I found my answer in the form of Bitwise operators.

For those who might be reading this, and don't know, the bitwise operator used is "or".

you would write:

newPermission=old1perm|old2perm; (bitwise "or")

1000|0001=1001
1100|1001=1101