b$)($i$)$ Convert the following decimal numbers into their binary equivalents without using a calculator. All workings must be shown.

$500\mathrm{.}510$

${100\mathrm{.}1}_{10}$

$($ii$)$ Convert the same numbers in question $1$b$)($i$)$ into their hexadecimal

$2$

$($base sixteen$)$ equivalents.