I need a full answer please with explanaing clearly

(20 points) Filtered Linear Feedback Shift Register basics. In this exercise we consider the following filtered LFSR. S1 S2 S3 84 $5 S6 mux 20 21 22 ... (a) Given an initial state s = (1,0,0,1,1,0,0,1,1), what are the first five output bits? (Outputs occur just before iterating the filtered LFSR.] (b) The multiplexer here outputs z = sa where A is determined by A = 1 + $5 + 256. Express the output function for z in terms of so, ...,S6 (20 points) Filtered Linear Feedback Shift Register basics. In this exercise we consider the following filtered LFSR. S1 S2 S3 84 $5 S6 mux 20 21 22 ... (a) Given an initial state s = (1,0,0,1,1,0,0,1,1), what are the first five output bits? (Outputs occur just before iterating the filtered LFSR.] (b) The multiplexer here outputs z = sa where A is determined by A = 1 + $5 + 256. Express the output function for z in terms of so, ...,S6