Suppose $A$ and $B$ two different binary strings of length $l$. Suppose the Mutual Information (https://en.wikipedia.org/wiki/Mutual_information) of $A$ and $B$ is known to be $I$.
Now suppose bit-wise a Boolean function is applied to get another bit-string $C$. The Boolean function is $f(0,0)=0, f(0,1)=0, f(1,0)=0, f(1,1)=1$.
Under this function f, what would be the Shannon entropy of the bit-string $C$? I want to know the least upper bound and greatest lower bound of the Shannon entropy.
Thanks in advance.