As an example of binary $($base$-2),$ consider your computer$$s Internet Protocol $($IP$)$ address. An IP is like your home mailing address, uniquely identifying where a computer is in a network of computers. IP addresses are $32-$bit binary numbers, commonly expressed in the dotted$-$decimal format in which the $32$ bits are grouped into four bytes $($each byte has $8$ bits$).$

So the IP address $129\mathrm{.}10\mathrm{.}116\mathrm{.}200$ is equivalent to $10000001$:$00001010$:$01110100$:$11001000$ in binary, and equivalent to $0$x$810$A$74$C$8$ in hex. Note that $129\mathrm{.}10\mathrm{.}116\mathrm{.}200,12910116200.$

$($a$)[10$ points$]$ Suppose your IP address is $3$C$\mathrm{.}82.$EA$\mathrm{.}54$ in hex. Determine your IP address, both in binary and also in dotted$-$decimal format. Show your work.