Floating number $(5pt)$

Write down the binary representation of the decimal number $63\mathrm{.}25$ assuming

the IEEE $754$ double precision format.

Calculate the sum of $2\mathrm{.}612510$ and $4\mathrm{.}150390625{10}^{-1}$ by hand, assuming $A$

and $B$ are stored in the $16-$bit half precision where the leftmost bit is the sign

bit, the exponent is $5$ bits wide and has a bias of $15,$ and the mantissa is $10$ bits

long, and a hidden $1$ is assumed. Assume $1$ guard, $1$ round bit, and $1$ sticky bit,

and round to the nearest even. Show all the steps.