Convert $-5\mathrm{.}33$ to a $12-$bit IEEE floating point representation with a sign bit followed by a $5-$bit biased exponent. You may use $5\mathrm{.}33=101\mathrm{.}0101010001111010$ in your calculations. Determine the error in this representation if there is any. Show all working.

$[6$ marks$]$