For all problems, answers with incomplete solution $/$ answers that do not follow the given instruction, will not merit any points.

Number Systems $(10$ pts each$)$

a$.{1100\mathrm{.}01}_2+{55\mathrm{.}5}_8=$

b$.$ Convert ${3\mathrm{.}125}_{10}$ to single precision $32-$bit floating point.

Note: your final answer must be hexadecimal format.

c$.$ Determine the $2\text{'}$s complement of $(10101\mathrm{.}101{)}_2$

d$.$ Subtract using $(r-1)\text{'}$s complement: ${10101\mathrm{.}01}_2-{1100\mathrm{.}1}_2$

e$.$ Encode the word EK$1$ in ASCII code with an odd parity bit added to the leftmost bit of every letter.

Note: your final answer must be hexadecimal format.

Boolean Algebra: K Map solutions will not merit any points.

a$.$ Simplify to minimum number of literals:

i$.A{B}^{\text{'}}C{D}^{\text{'}}+B^{\text{'}}C{D}^{\text{'}}+A{B}^{\text{'}}C{D}^{\text{'}}+A{B}^{\text{'}}{D}^{\text{'}}$

ii$.F(x,Y,Z)=(0,1,4,5,8,9)$

b$.$ Find the complement of the given function and simplify in POS format

i$.F(W,x,Y,Z)={\displaystyle \underset{?}{\overset{?}{}}}(2,3,6,7,10,11)$

c$.$ Convert to Product of Maxterms. NOTE: Your final answer must be in numerical format $F(A,B,C,D)=A+B{C}^{\text{'}}$

d$.$ Using Boolean Algebra, find the Simplified Boolean Expression for $F$