$($Answers to problems marked with $*$ appear at the end of the text.$)$

$1\mathrm{.}1$ List the octal and hexadecimal numbers from $16$ to $32.$ Using A and B for the last two digits, list the numbers from $8$ to $28$ in base $12.$

$1\mathrm{.}2*$ What is the exact number of bytes in a system that contains $($a$)32K$ bytes, $($b$)64M$ bytes, and $($c$)6\mathrm{.}4$G bytes?

$1\mathrm{.}3$ Convert the following numbers with the indicated bases to decimal:

$($a$)(4310{)}_5$

$($b$)(198{)}_{12}$

$($c$)(435{)}_8$

$($d$)(345{)}_6$

$1\mathrm{.}4$ What is the largest binary number that can be expressed with $16$ bits? What are the equivalent decimal and hexadecimal numbers?

$1\mathrm{.}5*$ Determine the base of the numbers in each case for the following operations to be correct:

$($a$)\frac{14}{2}=5$

$($b$)\frac{54}{4}=13$

$($c$)24+17=40.$

$1\mathrm{.}6*$ The solutions to the quadratic equation $x^2-11x+22=0$ are $x=3$ and $x=6.$ What is the base of the numbers?