The point is to not think of the bits as the representation of a decimal number. For example, if I need to know in which quadrant an angle is, I just need to look at the first two bits, independently of the precision (which we change just shifting and truncating). But I do not mind if 90 degrees are equal to 64 or 1073741824 "sectors".

I think this is another good example where a binary representation (and a shift) can be a more natural way to approach the problem.