A Boolean function F is called self-dual if and only if F(x₁, x₂, ......., xₙ) = F(x₁', x₂', ....., xₙ')
A Boolean function F is called self-dual if and only if
F(x₁, x₂, ......., xₙ) = F(x₁', x₂', ....., xₙ')
How many Boolean function of degree n are self-dual ?
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Correct answer: (D) (2)^(2^(n−1))
Explanation
A self-dual function is fixed by its values on one half of the input combinations: the 2ⁿ input combinations form 2ⁿ⁻¹ mutually complementary pairs, and the function's value on one member of each pair determines its value on the other. So the number of self-dual functions is 2^(2^(n−1)).