Question $1$:

We would like to present numbers in base $K$ in a new form. The number $x$ which is an $n$ digits base $K$ number will be given by:

$(x{)}_K=(x_{n-1},$dots,$x_2,x_1,x_0{)}_K$

The digit $x_i$ is represented in $2\text{'}$s complement using $|$~$lo{g}_2((K))$~$|$ bits when the range of values of $x_i$ is from $-{|}_{{?}_{?}}\frac{K}{(2{)}_{{?}_{?}}}|$ to $K-1-{|}_{{?}_{?}}\frac{K}{(2{)}_{{?}_{?}}}|.$

If$,$ for example, $K=3$ then $2=|$~$lo{g}_2(3)$~$|$ and all possible values of $x_i$ are $($:$1,1$:$)=(-1)$ or $($:$0,0$:$)=0$ or $($:$0,1$:$)=1.$

If $K=4$ then $2=|$~$lo{g}_2(4)$~$|$ and all possible values of $x_i$ are or or $($:$0,0$:$)=0$ or $($:$0,1$:$)=1.$

The value of the number $(x{)}_K$ is given by:

$x={\displaystyle \underset{i=0}{\overset{n-1}{}}}{x}_i*K^i$

$1\mathrm{.}4)$ Find the rule for negating the number. If there are cases in which the negated value is out of the possible range, choose the closet possible value. Prove your answer.

$1\mathrm{.}5)$ We would like to design a Full Adder component for $K=3.$

Here is the drawing of that component: