Question$1$

$($a$)$ Convert $-2\mathrm{.}625$ to an $8-$bit floating point representation as shown in lecture. $($In other words,what is the $8$ bit floating point equivalent of this decimal value?$)$ Write your answer in binary.Show your work, include the sign bit, exponent, and mantissa!

$($b$)$ Convert the $8-$bit floating point number $1110,0111$ to its decimal equivalent. Assuming afloating point representation of $8$ bits as shown in lecture, what is the decimal equivalent?show your work!

$($c$)$ Which of the following computations will overflow? Both inputs and the output are $8-$bit $2\text{'}$s complement, so for subtraction we mean subtracting one $2\text{'}$s complement number from anotr of which either or both can be negative themselves. $($Write $\text{'}$ Y $\text{'}$ if overflow will occur, $\text{'}$ N $\text{'}$ if not.$)11011100+01011111($Write $\text{'}$ Y $\text{'}$ if overflow will occur, $\text{'}$ N $\text{'}$ if not.$)11011100+11011111($Write $\text{'}$ Y $\text{'}$ if overflow will occur, $\text{'}$ N $\text{'}$ if not.$)11011100-01101011($Write $\text{'}$ Y $\text{'}$ if overflow will occur, $\text{'}$ N $\text{'}$ if not.$)$