$1.$ We will now analyze a pseudorandom number sequence generated by a LFSR characterized by $($p$2=1,$ p$1=1,$ p$0=0).$

a$.$ Draw the LFSR diagram.

b$.$ What is the sequence $($s$2,$ s$1,$ and s$0)$ generated from the initialization vector $($s$2=1,$ s$1=0,$ s$0=0)?$

c$.$ b$.$ What is the sequence $($s$2,$ s$1,$ and s$0)$ generated from the initialization vector $($s$2=0,$ s$1=1,$ s$0=1)?$

d$.$ How are the two sequences related?