Consider a $($binary$)$ floating point system of the form $(1.s_1{s}_2{s}_3{)}_2{2}^m$ where min$[-63,64].$ Calculate theConsider a $($binary$)$ floating point system of the form $(1.s_1{s}_2{s}_3{)}_2{2}^m$ where min$[-63,64].$ Calculate the

relative error, with respect to $2-$norm if we convert the vector $n{R}^2$ to the given floating point system.

When converting to floating point, first convert to a binary number then truncate any additional bits.

$x=\left[\begin{array}{c}3\mathrm{.}5000000\\ 4\mathrm{.}5000000\end{array}\right]$

Note: We are interested in the representation accuracy of floating point. So assume that all operations

performed $($addition$,$ subtraction, etc.$)$ do not increase the error.

relative error $(x)=$ number rtol $=0\mathrm{.}01,$ atol $=0\mathrm{.}001$

relative error, with respect to $2-$norm if we convert the vector $n{R}^2$ to the given floating point system.

When converting to floating point, first convert to a binary number then truncate any additional bits.

$x=\left[\begin{array}{c}3\mathrm{.}5000000\\ 4\mathrm{.}5000000\end{array}\right]$

We are interested in the representation accuracy of floating point. So assume that all operations

performed $($addition$,$ subtraction, etc.$)$ do not increase the error.

relative error $(x)=$ number rtol $=0\mathrm{.}01,$ atol $=0\mathrm{.}001$