Digital logic

Question

With 4 boolean variables, how many boolean expression & functions and combination can be formed?

Answer 1

Here we will proceed it in general suppose we have n boolian variable so for n boolian variable if we draw a k map then it have total 2^n blocks in that k map and in each k map block there are 2 possibilities either 1 or 0 so  total combination = (2)^2^n.
Now for r qestion n=4 so we have  (2)^2^n.=2^16 boolean expression as well as boolean functions also.

Comments

Maximum possible combinations $ = 2^{n},$ where $n = 4$
Maximum possible combinations $ = 2 ^{4} = 16$ and maximum possible functions $ = 2 ^ {2 ^ {n}},$ where $n = 4$
Maximum possible functions$ = 2 ^{2^{4}} = 2^{16}  = 65536$