$1.$How do a router and a switch differ? Please provide two differences.

$2.$ Given the code polynomial x$3+$x$+1,$ answer the following questions.

a$.$ Given the data bits $1101010011$ that need to be transmitted to a remote host, calculate the

message to be sent, including the CRC check bits. Be sure to show your work.

b$.$ The message $1001101011010$ which includes CRC check bits using the code polynomial

mentioned above, has been received by the remote host. Determine whether this message

contains any errors. Be sure to show your work.

$3.$ Node A and B are connected by a bi$-$directional optical link with $100$ Mb$/$s bandwidth and $400$ km distance in each direction: $($show your work$).$

There is no packet drops or queuing delays incurred. For the following, assume the speed of light in glass is $2\backslash$times $108$ m$/$s$.$ Also, $1$ Mb is $106$ bits. $($no need to reduce your answer$)$

a$-$ What is the link latency $($propagation delay$)$ of the A $->$B link?

b$-$ Suppose now that when A sends a $1000-$bit packet to B$,$ and whenever B receives the packet, it processes it for $200\backslash$mu s and then responds with an ACK packet of size $400$ bit. When does A receive B$$s ACK?

$4.$ Suppose a $1$Gbs point $-$to$-$point link is being set up between the Earth and a new lunar colony. The

distance from the moon to the Earth is approximately $385,000$ km$,$ and data travels over the link

at the speed of light $3$x$108$ m$/$s$.$

a$.$ Calculate the minimum RTT for the link.

b$.$ Using the RTT as the delay. calculate the delay x bandwidth product for the link.

c$.$ What is the significance of the delay x bandwidth product computed in $($b$)?$