a$)$ For a $16-$bit $\backslash (\backslash$mathrm$\{$A$\}/\backslash$mathrm$\{$D$\}\backslash )$ converter with an input voltage range of $-35$ V to $35$ V ; find

i$.$ signal resolution $($step size$).$

ii$.$ Dynamic range $($in dB $).$

iii. Quantization error for a $6$ V signal.

b$)$ Calculate the number of bits required for an ADC to encode $\backslash (\backslash$mathrm$\{$a$\}\backslash$pm $32\backslash$mathrm$\{$~V$\}\backslash )$ signal which has $3\mathrm{.}75$ mV sensitivity or system noise. $(4$p$)$