$(1$ point$)$ Note: The notation from this problem is from Understanding Cryptography

by Paar and Pelzl.

Suppose you have an LFSR with $6$ state bits. The first $12$ bits of output produced

by this LFSR are

$100001010001=s_0{s}_1{s}_2{s}_3{s}_4{s}_5{s}_6{s}_7{s}_8{s}_9{s}_{10}{s}_{11}.$

The first bit produced is the leftmost bit and the bit most recently produced is the

rightmost bit.

a$)$ What is the initial state of the LFSR$?$ Please enter your answer as unspaced

binary digits $($e$.$g$.010101$ to represent

$($:$s_5=0,s_4=1,s_3=0,s_2=1,s_1=0,s_0=1\}$

b$)$ What are the tap bits of the LFSR$?$ Please enter your answer as unspaced

binary digits $($e$.$g$.010101$ to represent

$p_5=0,p_4=1,p_3=0,p_2=1,p_1=0,p_0=1$