Question

How many bits are needed to express the integer n?

Answer 1

Start with a simple table.

Answer 2

Seems like we get a pattern \[
\lfloor\log_2(n+1)\rfloor
\]

Answer 3

count in base 2. since each bit represents the exponent of a power of 2

Answer 4

\[
\begin{array}{c|c|c}
n_{10}& n_2 & \#\text{ of bits}\\
0 &0&1\\
1&1&1\\
2&10&2\\
3&11&2\\
4&100&3\\
5&101&3\\
6&110&3\\
7&111&3\\
8&1000&4
\end{array}
\]

Answer 5

wio wouldn't you just add 1 after taking the floor instead including + 1 in the floor function?