Part $3.$ Optical switch design

$10.$ If a three$-$stage $256$ x $256$ Clos optical switch is used to route the data as in fig$\mathrm{.}1,$ the blocking probability will be:

a$)10-3$

b$)10-4$

c$)0$

d$)10-5$

$11.$ If the loss of each stage of the switch is $1$ dB$,$ what is the minimum insertion loss of the Clos optical switch in dB$?$

a$)100$

b$)10$

c$)3$

d$)6$

$12.$ You are now required to use $2$ x $2$ optical switches to make up a $128$ x $128$ optical switch. How many $2$ x $2$ switches are needed at the switch input?

a$)64$

b$)100$

c$)200$

d$)128$

$13.$ How many $2$ x $2$ switches are needed at the switch output?

a$)10$

b$)100$

c$)50$

d$)64$