$.$ Consider the decimal number $103\mathrm{.}4.$ For the following, please show your work:

$($a$)$ Convert this number to binary.

$($b$)$ Express this number as a normalized binary number.

$($c$)$ Determine the eleven exponent bits that encode p in the double precision binary

machine representation.

$($d$)$ Determine the $52$ bits that encode the mantissa in the double precision binary

machine representation. $($You will have to apply a rounding rule.$)$