$2.$ Answer the following questions w$.$r$.$t$.$ the data sequence: $10101000101110011010.$

Show your work clearly.

a$.$ Show the resulting waveforms using NRZ$,$ NRZI, and Manchester coding. Also show the clock signal for reference. Provide a right$-$to$-$the$-$point comparison $($pros and cons$)$ of these three schemes using specific examples from your results.

b$.$Determine the final transmitted bit stream using $2-$D $($even$)$ parity with $4$ rows of data $($and you will have a sixth row for parity$).$Give an example of a $1-$bit error and an example of a $2-$bit error and show how $2-$D parity can $($or cannot$)$ be used to detect and$/$or correct the errors.

c$.$ Use Cyclic Redundancy Check $($CRC$)$ with the divisor $1101$ to derive the transmitted bit sequence. Search for credible sources $($and cite them properly$)$ and provide a concise statement on how CRC can help detect $1-$bit errors, burst$-$errors, and multi$-$bit errors and use your bit sequence as examples to strengthen your statement.