Extracting rightmost N bits of an integer

Question

In the yester Code Jam Qualification round http://code.google.com/codejam/contest/dashboard?c=433101#s=a&a=0 , there was a problem called Snapper Chain. From the contest

Answer 1

Let's use N=3 as an example. In binary, 1<<3 == 0b1000. So 1<<3 - 1 == 0b111.

In general, 1< creates a number with N ones in binary form.

Let R = 1<. Then the expression becomes (K&R) == R. The K&R will extract the last N bits, for example:

     101001010
  &        111
  ———————————— 
     000000010

(Recall that the bitwise-AND will return 1 in a digit, if and only if both operands have a 1 in that digit.)

The equality holds if and only if the last N bits are all 1. Thus the expression checks if K ends with N ones.