The bit length 
of a positive integer 
is the number of binary digits
in its representation without leading zeros. It is given by
 |  |  |
(1)
|
 |  | ![[lg(n+1)],](/images/equations/BitLength/Inline8.svg) |
(2)
|
where ![[x]](/images/equations/BitLength/Inline9.svg)
is the ceiling
function, 
is the floor function, and 
denotes the binary logarithm
(see lg). Adopt 
by convention. For 
, 1, 2, ..., the sequence of
bit lengths is given by 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, ...
(OEIS A029837, with 
). The function is given by the Wolfram
Language function BitLength[n].
