The division algorithm in slide $17$ of lecture $5($Advanced Arithmetic Circuitries$)$

is called restoring division, since each time the result of subtracting the divisor

from the dividend is negative you must add the divisor back into the dividend

to restore the original value. Recall that shift left is the same as multiplying

by two. Let$$s look at the value of the left half of the Remainder again, starting

with step $3$b of the divide algorithm and then going to step $2$:

$($Remainder $+$ Divisor$)$ x $2-$ Divisor

This value is created from restoring the Remainder by adding the Divisor, shiting

the sum left, and then subtracting the Divisor. Simplifying the result we get

$2$

Remainder x $2+$ Divisor x $2-$ Divisor $=$ Remainder x $2+$ Divisor

Based on this observation, write a nonrestoring division algorithm using

the notation of the flowchart on slide $17$ that does not add the Divisor to the

Remainder in step $3$b$.$ Show that your algorithm works by dividing $(00000111)2$

by $(0010)2.$