Problem $3$: $(12$ Points$)$

Use the following diagram that represent LFSRs:

a$)$ Provide the polynomial representation for the above LFSRs$?$

b$)$ Starting with $0001$ initial state, show all unique states?

c$)$ What is the sequence of generated bits?

d$)$ What is the maximum period? Is the polynomial primitive?

e$)$ Show the LFSRs diagram that represent the polynomial X$8+$ X$3+1?$