$(15$ points$)$ Using $4-$bit numbers to save space, multiply $12$ten $*7$ten, or $1100$two $*0111$two.

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.

Iteration Step Multiplier Multiplicand Product

$0$ Initial Values $01110000110000000000$

$11$a: $1->$Prod$=$Prod$+$Mcand

$2.$ Shift left Mcand

$3.$ Shift right Mult

$21$a: $1->$Prod$=$Prod$+$Mcand

$2.$ Shift left Mcand

$3.$ Shift right Mult

$31$a: $1->$Prod$=$Prod$+$Mcand

$2.$ Shift left Mcand

$3.$ Shift right Mult

$41$a: $1->$Prod$=$Prod$+$Mcand

$2.$ Shift left Mcand

$3.$ Shift right Mult