Consider the Linear Feedback Shift Register $($LFSR$)$ of Figure Q$7.($a$)$ Describe two practical uses of LFSRs$,$ and discuss the properties which make them useful for these applications. $($b$)$ What is the maximal length of bit pattern associated with a LFSR with the same number of outputs as that of figure Q$7?($c$)$ State the criteria which must hold for a LFSR to be of maximal length. $($d$)$ Show, by using a characteristic polynomial or by any other means, that the pseudo$-$random sequence generated by this circuit is not of maximal length. $[8]($e$)$ Describe the operation and purpose of the logic gates labeled A and B in the operation of the circuit. $[8]$ Figure $\backslash ($ Q$^\{7\}\backslash )$