$1.)$What generalizations can you draw about converting a number from one base to a power of that base, e$.$g$.,$ from base $2$ to base $4(22)$ or base $8(23).$

$2.)$Convert the following binary numbers to their decimal equivalents:

$001100$ B$.000011$ C$.0111000$ D$.111100$ E$.101010$ F$.11100\mathrm{.}011$ G$.110011\mathrm{.}10011$ H$.1010101010\mathrm{.}1$

$3.)$Convert the following decimals to their binary equivalents: A$.64$ B$.100$ C$.111$ D$.145$ E$.255$ F$.34\mathrm{.}75$ B$.27\mathrm{.}1875$

$4.)$Briefly explain $($in detail$)$ the following representations: $1.$ sign magnitude $2.$ twos compliment $3.$ biased

$5.)$Explain how to determine if a number is negative in the following representations: $1.$ sign magnitude $2.$ twos complement $3.$ biased

$6.)$What is the sign extension rule for twos complement numbers?

$7.)$How can you form the negation of an integer in twos complement representation?

$8.)$What is the difference between the twos complement representation of a number and the twos complement of a number?

$9.)$What are the four essential elements of a number in floating$-$point notation?

$10.)$ What are the basic elements of floating$-$point addition and subtraction?