Consider a $32-$bit floating$-$point representation based on the IEEE floating$-$point format:

$$ the highest bit is used for the sign bit,

$$ the sign bit is followed by $5$ exponent bits, which are then

$$ followed by $26$ fraction bits.

$(1)$ Convert decimal value $-29\mathrm{.}21875$ into the above $32-$bit IEEE floating$-$point format. Write out the result in the hex$-$decimal format.