$1.[30$ points$]$ Consider the rdt$3\mathrm{.}0$ Finite State Machine $($FSM$)$ discussed in class. Build a rdt $3\mathrm{.}0$ Finite State Machine which sends packets numbered $\backslash (0,1,2\backslash ),$ and $3$ to a receiver, successively. You need to come up with states and the actions to transition between the states for a sender and a receiver FSM$.$ Please draw the sender FSM as well as the receiver FSM$.$ Do not submit hand$-$drawn solutions as there is potential for confusion. Either use Powerpoint or another digital design tool such as Draw.io to show your final solution.

$2.[10$ points$]$ Suppose Host A and Host B use a GBN protocol with window size $\backslash ($ N$=3\backslash )$ and a long$-$enough range of sequence numbers. Assume Host A sends six application messages to Host B and that all messages are correctly received, except for the first acknowledgment and the fifth data segment. Draw a timing diagram $($similar to Figure $3\mathrm{.}22),$ showing the data segments and the acknowledgments sent along with the corresponding sequence and acknowledge numbers, respectively. Please use Powerpoint or another tool to draw your solution clearly.

$3.\backslash ([\backslash$mathbf$\{10\}+\backslash$mathbf$\{10\}=\backslash$mathbf$\{20\}\backslash )$ points$]$ Consider the GBN protocol with a sender window size of $4$ and a sequence number range of $1,024.$ Suppose that at time $\backslash ($ t $\backslash ),$ the next in$-$order packet that the receiver is expecting has a sequence number of $\backslash ($ k $\backslash ).$ Assume that the medium does not reorder messages. Answer the following questions:

$($a$)$ What are the possible sets of sequence numbers inside the sender$\text{'}$s window at time $\backslash ($ t $\backslash )?$ Justify your answer.

$($b$)$ What are all possible values of the ACK field in all possible messages currently propagating back to the sender at time $\backslash ($ t $\backslash )?$ Justify your answer.