What is the minimum number of bits required to sample a signal with a range of 1 volt at a resolution of 1 millivolt?
Why An n-bit converter divides its full-scale range into 2^n steps, so resolution = full scale / 2^n. To resolve 1 mV over a 1 V span you need at least 1 V / 1 mV = 1000 distinct steps. Since 2^9 = 512 is too few and 2^10 = 1024 is just enough, 10 bits is the minimum.
Watch out The 8-bit choice gives only 256 steps, which works out to about 3.9 mV per step over a 1 volt range, far coarser than the 1 mV required.
Divide range by resolution, then find the power of 2 that covers it: 1000 steps needs 1024, so 10 bits.
A kilobyte is 1024 = 2^10. You need 1000 steps (1 V in 1 mV steps), so you need the kilobyte's 10 bits.