Q$1$ Given the divisor polynomial function $P(x)=x^4+x+1$ and the data in polynomial form is $D(x)=x^7+x^6+x^4+x^2+x$ :

find the message that will be sent using $($assuming CRC$(12,8))$:

a$)$ Modulo $2$ Arithmetic method

b$)$ Polynomial method

Q$2$ Explain the concept of multiplexing in data communication, detailing how multiple signals are combined for transmission over a single medium. Compare and contrast the three main types of multiplexing: Frequency Division Multiplexing $($FDM$),$ Time Division Multiplexing $($TDM$),$ and Wavelength Division Multiplexing $($WDM$),$ and provide examples of where each is commonly used?