In how many bits do I fit

JavaScript (ES6), 18 bytes

f=n=>n&&1+f(n>>>1)

<input type=number min=0 step=1 value=8 oninput="O.value=f(this.value)">
<input id=O value=4 disabled>

05AB1E, 2 bytes

bg

Try it online!

x86 Assembly, 4 bytes

Assuming Constant in EBX:

bsr eax,ebx
inc eax

EAX contains the number of bits necessary for Constant.

Bytes: ☼¢├@

Hexadecimal: ['0xf', '0xbd', '0xc3', '0x40']