EE $2741-$ Homework $5$

due Mon., Oct $28,2024$ in Moodle by $11$:$59$ pm

To enhance readability, the binary numbers include a space between each four bits.

$1.($a$)$ Convert $(121)\backslash (\{\}\_\{10\}\backslash )$ to binary, octal, and hexadecimal.

$($b$)$ Convert $(10010010)2$ into octal, hexadecimal, and decimal.

$2.$ Determine the $8-$bit sign$-$and$-$magnitude, $1\text{'}$s complement, and $2\text{'}$s complement representations for each of the following decimal numbers: $\backslash (+47,-80\backslash ).($Note: Be sure to represent $+47$ as a positive number and $-80$ as a negative number.$)$

$3.$ For each of the following numbers in $8-$bit $2\text{'}$s complement representation, determine the decimal value.

$($a$)00110101$

$($b$)10110101$

$4.$ Perform the following addition or subtraction of the given numbers using $8-$bit $2\text{'}$s complement representation of the numbers. Indicate in each case whether or not overflow occurs.

$($a$)\backslash (11010110+11000111\backslash )$

$($b$)\backslash (11010110-11000111\backslash )$