Design a gate$-$level $4-$bit multiplier. $[$Total $20$ points$]$

For the blocks you defined, describe the details just once.

Use labeled wires.

$($Hint: use $4-$bit adders to design your multiplier$)$

Inputs: a$0,$ a$1,$ a$2,$ a$3,$ b$0,$ b$1,$ b$2,$ b$3.$

Outputs: s$0,$ s$1,$ s$2,$ s$3,$ s$4,$ s$5,$ s$6,$ s$7$