$6.(20$ marks$)$ Let a LFSR be built with characteristic polynomial

f$($x$)=$ x$^4+$ x$^3+$x$2+$ x $+1.$

$($a$)(10$ marks$)$ Draw a diagram of the LFSR$.$

$($b$)(10$ marks$)$ Show the transition diagram for the LFSR$.$ What is the maximal period of its output sequences?

can you give me hhandwrittenproper solution with peoper diagram