$2.$ Perform the following floating$-$point multiplication problem in binary, using half$-$precision format.

$462\mathrm{.}50\mathrm{.}0375$

where

$462\mathrm{.}5$ has an IEEE $754$ encoding of $0$xdf$3$a$,$ and

$0\mathrm{.}0375$ has an IEEE $754$ encoding of $0$x$28$cd$.$

a$.$ At the end of the multiplication, rounding may be necessary to store the product in half$-$precision

format. What are the single bit values for the guard bit, round bit, and sticky bit.

b$.$ What is the decimal value of the product of multiplication after rounding the binary product in order to

fit the $10-$bit fraction of the half$-$precision format.

c$.$ What is the IEEE $754$ encoding of the product?