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']