$3$ A memory array $M$ with $n$ inputs containing bit words of length $m$ is properly a bit matrix of order $2^{n}m.$ Any row is indexed by an address which is a string of $n$ bits. The array $M$ can also be described by giving the $m$ Boolean functions $f_0,$dots,$f_{m-1}$ such that for each address ain$\{0,1{\}}^n$ and each column $b$ : $M_{ab}=f_b(a).$

Suppose that $m=n.$

a$.(10$ points.$)$ Find the Boolean functions $f_0,$dots,$f_{n-1}$ representing the $2^{n}n-$memory array such that each word is equal to the corresponding address.

b$.(10$ points.$)$ Find the Boolean functions $f_0,$dots,$f_{n-1}$ representing the $2^{n}n-$memory array such that at each address the word consists of repetitions of the least significant bit of the address:

$)=a_{n-1}cdots{a}_0$Longrightarroww$=(a_0^n$