Given the following decimal values for variables a and $b$ :

$a=125{10}^{-3}$

$b=2\mathrm{.}2{10}^3$

Instructions:

Convert the decimal values of a and $b$ into their IEEE $754$ standard binary

representation for double$-$precision floating$-$point format.

Execute the addition operation using the instruction add. $$f2,$$$f,$ $$f6,$

where:

Register $$f4$ contains the value of $a.$

Register $$f6$ contains the value of $b.$

After performing the addition, provide the binary representation of the

result stored in register $ $f2$ according to the IEEE $754$ standard for double$-$

precision floating$-$point numbers.

Q$3.$ In Floating Point representations, answer the following questions showing all

the steps: $($Use the IEEE $754$ standard for all$)($showing all the steps used$)$: $(35$

points$)$

a$)$ Write down the binary representation of the decimal number $31\mathrm{.}625$

b$)$ Write down the binary representation of the decimal number $31\mathrm{.}625$

assuming the IEEE $754$ double precision format.

c$)$ Write down the binary representation of the decimal number $45\mathrm{.}45.$

d$)$ Write down the binary representation of the decimal number $-19\mathrm{.}625.$

e$)$ What decimal number does the bit pattern $0C_{000000}$ represent if it

is a floating$-$point number?