algorithm - How to find if number 2^n is in sum of 2^1 - 2^m -

let's in system users' statuses assigned numbers powers of 2.

 1 - new member  2 - member  4 - friend  8 - vip 16 - admin 32 - system owner 

so if system owner got friend , admin statuses, status have value of 52. now, want query status table , see users have friend status. how check number 4 part of number-generating sum (52)?

if done function, following output expected:

ispartof( 4, 52);   //returns true ispartof(12, 52);   //returns false since 8 (vip) not used during calculating 52 

algorithm comes mind subtraction of maximum possible number (2^n) lower (in example case) 52. there more efficient way this?

bitwise and.

>>> 52 & 4 == 4 true >>> 52 & 12 == 12 false