A Boolean function of n variables is a mapping f : {0, 1}^n to {0, 1}. . Determine the number of Boolean functions f of n variables such that

(i) f is not self-dual and f(0, 0, . . . , 0) = f(1, 1, . . . , 1),

(ii) f is self-dual and f(0, 0, . . . , 0) = 1.

I think for the first part, i need to find the number of functions that is not self-dual, then find the number of functions i need from it? For the second part,i absolutely have no clue, please help me with this question.