$3.(10$ pts$)$ A $0-$to$-10$ V$,4-$bit successive approximation A$/$D converter is used to measure an

input voltage.

a$)(3$ pts$)$ Determine the quantization error of the A$/$D converter.

b$)(3$ pts$)$ For an analog voltage input of $2\mathrm{.}9$ V$,$ determine the binary representation and

corresponding digital output voltage.

c$)(4$ pts$)$ What number of bits would the A$/$D converter need to ensure a reading within

$2\mathrm{.}5$ mV of the actual output voltage?