$1.(10$ points$)$ Sketch the NRZ$,$ Manchester, and NRZI encoding for the bit stream $010111110000.$ Assume that the NRZI signal starts out low.

$2.(5$ points$)$ show the $4$B$/5$B encoding, and the resulting NRZI signal, for the following bit sequence: $0000000101011111$

$3.(20$ points$)$ For a sliding window algorithm with SWS$=5$ frames and RWS$=5$ frames, the receiver use cumulative ACKs. Use a timeout interval of about $2$ x RTT$.$ Assuming that the transmit time of a frame is equal to $0\mathrm{.}2$ RTT and the frames are processed instantaneously if they arrive in order.

$1)(2$ pts$)$ What is the maximum number of frames that can be transmitted in one RTT$?$

$2)(2$ pts$)$ What is the smallest value for MaxSeqNum $($the number of available sequence number$)?$

$3)(8$ pts$)$ Draw a timeline diagram $($up to frame $7)$ for the situation when the Frame $2$ is lost. Note, frame number starts at $0.$

$4)(8$ pts$)$ Now, assume that the receiver sends a duplicate acknowledgement if it does not receive the expected frame. For example, it send DUPACK$[2]$ when it expects to see FRAME$[2]$ but receives FRAME$[3]$ instead. Retransmission takes place either upon receipt of the first DUPACK or upon timeout. Draw a timeline diagram $($up to frame $7)$ for the situation when the Frame $2$ is lost.

Note for part $3$&$4$: On each data frame and ACK frame, you need to indicate the sequence number $($start from $0).$ In addition, you need to indicate what action is taken by the receiver when a frame is received, for example, processed, buffered, or discarded.

$4.(10$ points$)$ Suppose that we run the sliding window algorithm with SWS $=9$ and RWS $=7,$ and no out$-$of$-$order arrivals.

$1)$ Find the smallest value for MaxSeqNum. No explanation

$2)$ For this condition, give an example showing that MaxSeqNum $1$ is not sufficient

$3)$ State a general rule for the minimum MaxSeqNum in terms of SWS and RWS$.$

$5.(10$ points$)$ Suppose you are designing a sliding window protocol for a $10$ Mbps point$-$to$-$point link to the moon, which has a one$-$way latency of $1\mathrm{.}25$ seconds. Assuming that each frame carries $80$KB of data, what is the minimum number of bits you need for the sequence number if RWS $=$ SWS$?$

$6.(10$ points$)$ Consider building a CSMA$/$CD $($the same protocol as Ethernet$)$ network running at $100$Mbps over a $200$ meter cable with no repeaters. The signal propagation speed in the cable is $2\mathrm{.}5$ x $108$ meter$/$sec$.$ What is the minimum frame size in order to be able to detect collisions?

$7.(15$ points$)$ Suppose two nodes, A and B$,$ are attached to opposite ends of a $1000$ meter cable, and that they each have one frame of $12,000$ bits $($including all headers$)$ to send to each other. Both nodes attempt to transmit at time t $=0.$ Suppose there are three repeaters between A and B$,$ each inserting a $20-$bit $($or $20$ bit$/10$Mbps $=2$ microseconds$)$ delay. Assume the transmission rate is $10$Mbps$,$ and CSMA$/$CD with backoff intervals of multiples of $512$ bits is used. After the first collision, A draws K $=0$ and B draws K $=1$ in the exponential backoff protocol. Ignore the jam signal and the $96-$bit time delay.

a$)$ What is the one$-$way propagation delay $($including repeater delays$)$ between A and B$?$ Assume that the signal propagation speed is $2$ x $108$ m$/$s$.$

b$)$ At what time is A$$s packet completely delivered at B$?$

c$)$ Now suppose that only A has a packet to send and that the repeaters are replaced with switches. Suppose that each switch has a $20-$bit processing delay in addition to a store$-$and$-$forward delay $($retransmission$).$ At what time, is A$$s packet delivered at B$?$ give me the correct solutions for all these questions.