Convert the following to $8-$bit two's complement$-$encoded binary integers and perform the indicated operations. You must show all conversions into and out of two's complement encoding. Provide your results in $8-$bit two's complement binary and base$-10$ or base$-16,$ as requested: $(0\mathrm{.}4$ points$)$

$($a$){27}_{10}-{15}_{10}$