Answer:
12 bits
Explanation:
With 12 bits you can represent numbers from 0 to 2¹²-1, i.e. 0 to 4095.
To check: with 11 bits you can only represent up to 2047, so that's not enough.
In general, to calculate the number of bits without trial and error, you can take the ²log of the number you want to represent and then round up:
²log(3001) = log(3001)/log(2) ≈ 11.55, rounded up is 12.
