$(15$ pts$)$ Floating point calculation:

a$.$ Show the IEEE $754$ representation for the decimal value $-2\mathrm{.}25$ in single precision.

b$.$ Find the decimal representation for the following single precision floating point number:

$1100,0000,1101,1000,0000,0000,0000,0000$

c$.$ Perform the addition and multiplication of the two floating point numbers in $($a$)$ and $($b$)$ in binary scientific notation, and represent the sum and product in single precision.