 Uniform quantization error

rounding an unclipped voltage to equally spaced levels of separation $\Delta$ leaves error in $[-\Delta /2,\Delta /2]$. If the fractional position within a conversion interval is uniformly distributed, direct integration gives zero mean and expectation value $⟨{ϵ}^2⟩={\Delta }^2/12$. This is a statistical model for the error, not a claim that the converter adds independent white noise for every possible input.