Problems

$1\mathrm{.}1$ Convert to hexadecimal and then to binary:

$($a$)757\mathrm{.}2510$

$($b$)123\mathrm{.}17,0$

$($c$){356\mathrm{.}89}_{10}$

$($d$){1063\mathrm{.}5}_{10}$

$1\mathrm{.}2$ Convert to octal. Convert to hexadecimal. Then convert both of your answers to decimal, and verify that they are the same.

$($a$){111010110001\mathrm{.}011}_2$

$($b$){10110011101\mathrm{.}11}_2$

$1\mathrm{.}3$ Convert to base $6$:$3BA{\mathrm{.}25}_{14}($do all of the arithmetic in decimal$).$

$1\mathrm{.}4($a$)$ Convert to hexadecimal: ${1457\mathrm{.}11}_{10}.$ Round to two digits past the hexadecimal point.

$($b$)$ Convert your answer to binary, and then to octal.

$($c$)$ Devise a scheme for converting hexadecimal directly to base $4$ and convert your answer to base $4.$

$($d$)$ Convert to decimal: DEC.A $16{?}^{.}$

$1\mathrm{.}5$ Add, subtract, and multiply in binary:

$($a$)1111$ and $1010$

$($b$)110110$ and $11101$

$($c$)100100$ and $10110$

$1\mathrm{.}6$ Subtract in binary. Place a $1$ over each column from which it was necessary to borrow.

$($a$)11110100-1000111$

$($b$)1110110-111101$

$($c$)10110010-111101$

$1\mathrm{.}7$ Add the following numbers in binary using $2\text{'}$s complement to represent negative numbers. Use a word length of $6$ bits $($including sign$)$ and indicate if an overflow occurs.

$($a$)21+11$

$($b$)(-14)+(-32)$

$($c$)(-25)+18$

$($d$)(-12)+13$

$($e$)(-11)+(-21)$

Repeat $($a$),($c$),($d$),$ and $($e$)$ using $1\text{'}$s complement to represent negative numbers.

$1\mathrm{.}8$ A computer has a word length of $8$ bits $($including sign$).$ If $2\text{'}$s complement is used to represent negative numbers, what range of integers can be stored in the computer? If $1\text{'}$s complement is used? $($Express your answers in decimal.$)$

$1\mathrm{.}9$ Construct a table for $7-3-2-1$ weighted code and write $3659$ using this code.

$1\mathrm{.}10$ Convert to hexadecimal and then to binary.

$($a$){1305\mathrm{.}375}_{10}$

$($b$){111\mathrm{.}33}_{10}$

$($c$){301\mathrm{.}12}_{10}$

$($d$){1644\mathrm{.}875}_{10}$

$1\mathrm{.}11$ Convert to octal. Convert to hexadecimal. Then convert both of your answers to decimal, and verify that they are the same.

$($a$){101111010100\mathrm{.}101}_2$

$($b$){100001101111\mathrm{.}01}_2$