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Boolean function is described by it's truth table. More specifically - by it's Y row. Consider 2-AND:
x1x2 y
0 0 0
0 1 0
1 0 0
1 1 1
As you can see, the function is determined by the Y vector (bit vector), which has a length of 2^n. And, as you should now, a binary vector of length 2^n can take 2^(2^n) possible states.
That's it!
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distinctly different boolean functions with n inputs?