"""

Let y0, y1, y2,... be a sequence of random unsigned 32 bit integers
(i.e. 0 ≤ yi &lt; 232, every value equally likely).
For the sequence xi the following recursion is given:x0 = 0 and
xi = xi-1| yi-1, for i &gt; 0. ( | is the bitwise-OR operator)
It can be seen that eventually there will be an index N such that xi = 232 -1 (a bit-pattern of all ones) for all i ≥ N.
Find the expected value of N. 
Give your answer rounded to 10 digits after the decimal point.

"""