$2.$ The hypothetical computer, Shelly$-32$ has word lengths of $32$ bits $(32$ binary digits$).$ The bits composing a word in Shelly$-32$ are allocated in the following way when representing a nonzero real number x $=$q $\backslash$times $2"$:

Sign of real number x:

$1$ bit

$($#$31)$

Biased exponent:

$8$ bits

$($#$23-30)$

Mantissa

$23$ bits

$$#$022$

Express the number $1107\mathrm{.}34375$ as a $32$ bit word in Shelly$-32.$