$1.$ This problem concerns binary representations. Complete the follow$-$

ing, in each case describing how you arrive at your answer.

$($a$)$ How many integers can be represented using nine binary digits?

$($b$)$ What is the smallest nine$-$bit integer? What is the largest nine$-$

bit integer?

$($c$)$ What is the minimum number of binary digits needed to represent

the integer $250000?($note: you can answer this without finding the full

binary representation of $250000)$