Suppose there exists a $12-$bit IEEE $754$ floating point format, with $1$ sign bit, $6$ exponent bits, and $5$ fraction bits. Answer the following $3$ sub$-$questions below.

$($i$)$ How would $\backslash$infty be represented in this $12-$bit format? Show its $12-$bit representation

$($ii$)$ How would the smallest positive normalised number be represented? Show its $12-$bit representation

$($iii$)$ Give the nearest representation n of $5\mathrm{.}612$ in this format.