If a $2-$bit ADC is replaced by a $4-$bit ADC in a system, by what factor will the delta value $($amplitude quantized voltage$)$ decrease i$.$e$.,\frac{{}_{2-\text{b}\text{i}\text{t}\text{A}\text{D}\text{C}}}{{}_{4-\text{b}\text{i}\text{t}\text{A}\text{D}\text{C}}}?$

A designer wishes to build a circuit with $n-$bit ADC to sample and quantise the input signal. However, the input signal has an error $+-0\mathrm{.}001V$ because of external interference. Now, what should be the minimum value of $\text{'}n\text{'}$ such that $n-$bit ADC is robust to the error and the delta is at least $5$ times larger than the error? Assume that the ADC is designed for the input voltage range of $0$ to $1$ V $.$