E7F06

PRACTICAL CIRCUITS · Software defined radio fundamentals: digital signal processing (DSP) filtering, modulation, and demodulation; analog-digital conversion; digital filters

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What is the minimum number of bits required to sample a signal with a range of 1 volt at a resolution of 1 millivolt?

A4 bits
B6 bits
C8 bits
D10 bits

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.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

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