In IEEE $754$ standard, a single precision representation uses $32$ bits, in

which $1$ bit is used for the sign and $8$ bits are used for the exponent with

bias $127.$

$($a$)10\%$ What is the corresponding decimal number for the following

data with IEEE $754$ standard: $01000010011000000000000000000000?$

You have to show your derivation.

$($b$)10\%$ What is the corresponding IEEE $754$ single representation for the

negative decimal number $-3\mathrm{.}375?$ You have to show your derivation.