a$.(8$ pt$.)$ Calculate the digital output value of $7-$bit $\frac{A}{D}$ converter with voltage reference range to $+4V$ if the analog input voltage is $+3\mathrm{.}5$ V $.$

b$.(10$ pt$.)$ PIC$16$F$84$A works with $32$ MHz oscillator. It needs to generate a delay of $500ms$ using TMR$0$ register. The timer starts always from $6$ and works with $1$:$16$ pre$-$scalar.

$1-$ How many increments in TMR$0$ are required to generate $500$ ms delay?

$2-$ How many TMR$0$ overflow interrupts are required to generate $500$ ms delay?