We need to design a switch with $100$ input lines and $100$ output lines.

a$.$ If a crossbar switch has $100$ input lines and $100$ output lines, how many crosspoints

will it have?

b$.$ How many crosspoints will there be if the above crossbar switch is replaced with a

three$-$stage switch? You may consider the following specifications:

$$ Each switch in the first stage and last stage has $10*$ crosspoints.

$$ The middle stage has $4$ crossbars each with $10*10$ crosspoints