$($Q$\mathrm{.}1)$ Division PLEASE DO $6$ BITS for DIVISOR AND $12$ FOR REMAINDER!!

$1.$a$)$ Using the hardware described in the figure below, calculate $69$ divided by $21.$ In the hardware, choose an adequate N value. N bits are used in divisor and $2$ xN in the remainder.

$1.$b$)$ Check your results. Are the results correct? How many cycles of the algorithm are necessary to obtain the result? How is this number related to the operands and their size in bits?