PROBLEMS

$($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$)6\mathrm{.}4G$ 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?

$34$ Chapter $1$ Digital Systems and Binary Numbers

$1\mathrm{.}7*$ Convert the hexadecimal number $64CD$ to binary, and then convert it from binary to octal.

$1\mathrm{.}8$ Convert the decimal number $431$ to binary in two ways: $($a$)$ convert directly to binary;

$($b$)$ convert first to hexadecimal and then from hexadecimal to binary. Which method is faster?

$1\mathrm{.}9$ Express the following numbers in decimal:

$($a$)**(10110\mathrm{.}0101{)}_2$

$($b$)(16\mathrm{.}5{)}_{16}$

$($c$)**(26\mathrm{.}24{)}_8$

$($d$)($ DADA.$B{)}_{16}$

$($e$)(1010\mathrm{.}1101{)}_2$

$1\mathrm{.}10$ Convert the following binary numbers to hexadecimal and to decimal: $($a$)1\mathrm{.}10010,($b$)110\mathrm{.}010.$ Explain why the decimal answer in $($b$)$ is $4$ times that in $($a$).$

$1\mathrm{.}11$ Perform the following division in binary: $111011101.$