Question 29.2: Determine the effective number of bits for a resistor-string......

Using Eq. (29.10), the maximum INL will be

\left|{I}N L\right|_{m a x}=\frac{V_{R E F}}{2^{N}}\cdot \sum\limits_{k=1}^{2^{N-1}}{\frac{\Delta R_k}{R} } =\frac{V_{REF}}{2^{N}} \cdot \frac{2^{N-1}\cdot \Delta R_k}{R} =\frac{1}{2}\ LSB\cdot 2^N\cdot (\%\ \text{matching}) =0.01V_{REF}          (29.10)

Since we know that this maximum INL should be equal to ½ LSB in the worst case,

and solving for N yields

This means that the resolution for a DAC containing a resistor string matched to within 1% will be, at most 6 bits.