Assuming that we are working in a machine where only $3$ bits are allocated for storing the mantissa. Suppose the Rounding to Nearest Rule is used in this machine, i$.$e$.(1\mathrm{.}00111{)}_2{2}^3$ will be stored as $(1\mathrm{.}010{)}_2{2}^3.$ Compute $($a$)\frac{4}{7}+\frac{1}{4},$

$($b$)\frac{4}{7}\frac{1}{4}$

In each computation, solve the problem

$($i$)$ exractly

$($ii$)$ using the three$-$digit rounding arithmetic

$($iii$)$ compute the absolute errors in part $($ii$)$