$1\mathrm{.}7$ How many different numbers can be represented with $16$ bits? $(5$pts$)$

$65,536$ different numbers can be represented with $16$ bits. $(2^{16})$

$1\mathrm{.}10$ What is the largest $32-$bit binary number that can be represented with $(5$ pts$)$

$($a$)$ unsigned numbers?

$($b$)$ two's complement numbers?

$($c$)$ sign$/$magnitude numbers?