Problem $1$

Convert the following base$-2$ numbers to base$-10$:

$($a$)(101101)2$

$($b$)(101\mathrm{.}011)2$

$($c$)(0\mathrm{.}01101)2$

Problem $2$

Convert the following base$-8$ numbers to base$-10$:

$($a$)(71263)8$

$($b$)(3\mathrm{.}147)8$

Problem $3$

Convert the following base$-10$ numbers to base$-2$:

$($a$)141$

$($b$)141\mathrm{.}625$

Problem $4$

$($a$)$ Evaluate the polynomial:$32$

$560\mathrm{.}55$y x x x$=++$

at x $=1\mathrm{.}37.$ Use $3$ digits arithmetic with chopping. Evaluate the percent relative error.

$($b$)$ Repeat part $($a$)$ when y is expressed as:$()$

$()$

$560\mathrm{.}55$y x x x$=++$

$($c$)$ Compare the values of the percent relative error for both cases and comment on the results.