Problem $6(15$pts$)$: Consider the Cyclic Redundancy Check $($CRC$)$ algorithm discussed in class. Suppose that the $4$bit generator $\backslash ((\backslash$mathrm$\{$G$\})\backslash )$ is $1001,$ that the data payload $($D$)$ is $10001011$ and that $\backslash (\backslash$mathrm$\{$r$\}=3\backslash ).$

a$)$ What are the CRC bits $($R$)$ associated with the data payload of $\backslash ($ D $\backslash )?$

b$)$ Write the transmitted bit sequence, including the CRC bits.