$1$ Convert the following binary numbers to decimal:

$($a$)11$

$($b$)100$

$($c$)111$

$($d$)1000$

$($e$)1001$

$($f$)1100$

$($g$)1011$

$($h$)1111$

$2$ Convert the following binary numbers to decimal:

$($a$)1110$

$($b$)1010$

$($c$)11100$

$($d$)10000$

$($e$)10101$

$($f$)11101$

$($g$)10111$

$($h$)11111$

$3$ Convert each binary number to decimal:

$($a$)110011\mathrm{.}11$

$($b$)101010\mathrm{.}01$

$($c$)1000001\mathrm{.}111$

$($d$)1111000\mathrm{.}101$

$($e$)1011100\mathrm{.}10101$

$($f$)1110001\mathrm{.}0001$

$($g$)1011010\mathrm{.}1010$

$($h$)1111111\mathrm{.}11111$

$4$ What is the highest decimal number that can be represented by each of the following numbers of binary digits $($bits$)?$

$($a$)$ two

$($b$)$ three

$($c$)$ four

$($d$)$ five

$($e$)$ six

$($f$)$ seven

$($g$)$ eight

$($h$)$ nine

$($i$)$ ten

$($j$)$ eleven

$5$ How many bits are required to represent the following decimal numbers?

$($a$)17$

$($b$)35$

$($c$)49$

$($d$)68$

$($e$)81$

$($f$)114$

$($g$)132$

$($h$)205$