$2$A$)$ A CRC is constructed to generate a $4-$bit FCS for a $10-$bit message. The generator polynomial is

$x^4+x^3+x^2+1.$ Encode the data bit sequence $1001101110$ using the generator polynomial and give

the code word by using modulo $2$ arithmetic and verify at receiver's end.

$2$B$)$ A system uses the Stop$-$and$-$Wait ARQ Protocol. If each frame carries $1000$ bits of data, estimate

the time it take to send $2$ million bits of data if the distance between the sender and receiver is $6000$

Km and the propagation speed is $2108m.$ Ignore transmission, waiting, and processing delays.

We assume no data or control frame is lost or damaged.

$2$C$)$ Consider a channel with a $2-$MHz capacity and an SNR of $18$ dB $.$

a$)$ What is the upper limit to the data rate that the channel can carry?

b$)$ How many signal levels are needed to achieve this channel capacity?