A 10-bit counting A/D converter has an analog input in the range \(0 \leq v_{A} \leq\) \(5 \mathrm{~V}\) and has a clock frequency of \(1 \mathrm{MHz}\).

(a) What is the maximum conversion time?

(b) If the output is 0010010010 , what is the range of the input signal \(v_{A}\) (assume a quantization error of \(\pm \frac{1}{2}\) LSB).

(c) How many clock pulses are required to produce an output of 0100100100 ?