$(10$ points$)$ Consider a miniature binary computer whose floating$-$point words consist of $4$ binary $($i$.$e$.,$ base$-2)$

digits for the mantissa and $3$ binary digits for the exponent $($plus sign bits$).$ Let

x $=(\mathrm{.}1011)2\backslash$times $20,$ y $=(\mathrm{.}1100)2\backslash$times $20.(1)$

Mark in the provided table whether the machine operation indicated $($with the result Z assumed normalized$)$ is

exact, rounded $($i$.$e$.,$ subject to nonzero rounding error$),$ overflows, or underflows. Show your work.

Operation exact rounded overflow underflow

Z $=$ fl$($x $$ y$)$

Z $=$ fl$(($x $$ y$)8)$

Z $=$ fl$($x $+$ y$)$

Z $=$ fl$($y $+($x$/2))$

Z $=$ fl$($x $+($y$/16))$

$1$