thes

$5.(15$ points$)$ Using $4-$bit numbers to save space, multiply $\backslash (12\_\{\backslash$text $\{$ten $\}\}\{\}^\{*\}7\_\{\backslash$text $\{$ten$,\}\}\backslash )$ or $\backslash (1100\_\{\backslash$text $\{$two $\}\}\{\}^\{*\}0111\_\{\backslash$text $\{$two $\}\}\backslash ).$ Use the algorithm outlined in the flowchart in figure $3\mathrm{.}4$ and fill in what numbers, in the table, would populate in the Multiplier, Multiplicand, and Product in each step of each iteration.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Iteration & Step & Multiplier & Multiplicand & Product $\backslash \backslash$

$\backslash$hline $0$ & Initial Values & $0111$ & $00001100$ & $00000000\backslash \backslash$

$\backslash$hline $1$ & $1$a: $1->$Prod$=$Prod$+$Mcand & & & $\backslash \backslash$

$\backslash$hline & $2.$ Shift left Mcand & & & $\backslash \backslash$

$\backslash$hline & $3.$ Shift right Mult & & & $\backslash \backslash$

$\backslash$hline $2$ & $1$a: $1->$Prod$=$Prod$+$Mcand & & & $\backslash \backslash$

$\backslash$hline & $2.$ Shift left Mcand & & & $\backslash \backslash$

$\backslash$hline & $3.$ Shift right Mult & & & $\backslash \backslash$

$\backslash$hline $3$ & $1$a: $1->$Prod$=$Prod$+$Mcand & & & $\backslash \backslash$

$\backslash$hline & $2.$ Shift left Mcand & & & $\backslash \backslash$

$\backslash$hline & $3.$ Shift right Mult & & & $\backslash \backslash$

$\backslash$hline $4$ & $1$a: $1->$Prod$=$Prod$+$Mcand & & & $\backslash \backslash$

$\backslash$hline & $2.$ Shift left Mcand & & & $\backslash \backslash$

$\backslash$hline & $3.$ Shift right Mult & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$