Problem $1$: Rounding Errors

Compute the operation below by hand in IEEE double precision computer arithmetic, using the Rounding to Nearest Rule. What answer do you get?

$(8\mathrm{.}77\mathrm{.}7)1$

$2.$ Write the binary version of $8\mathrm{.}7$ and $7\mathrm{.}7$ into double precision format $($with rounding rules applied$)$

$3.$ Compute the rounding error for $8\mathrm{.}7$ and $7\mathrm{.}7$

$4.$ Use the computed rounding error to perform the original arithmetic