Let $A=(1001{)}_2$ and $B=(1111{)}_2.$ Determine AxB using Booth's algorithm if $A$ is the multiplicand and $B$ is the multiplier.

Multiplicand: $1001$

$-$Multiplicand:

Multiplier. $1111$

$\backslash$table$[[$Iteration$,$Step,Product,Previous LSB$,$Action$],[0,-,00001111,0,$Initialize$],[1,1\mathrm{.}10,,0,$Subtract$],[1,1\mathrm{.}2,,1,$Shift$],[2,2\mathrm{.}11,,1,\backslash$table$[[$No$],[$action$]]],[2,2\mathrm{.}2,,1,$Shift$],[3,3\mathrm{.}11,,1,$No action$],[3,3\mathrm{.}2,,1,$Shift$],[4,4\mathrm{.}11,,1,$No action$],[4,4\mathrm{.}2,,0,$Shift$]]$