The dual of a Boolean function \(F(x_1,x_2,\dots,x_n,+, .,')\) written as…
2014
The dual of a Boolean function \(F(x_1,x_2,\dots,x_n,+, .,')\) written as \(F^D\) is the same expression as that of \(F\) with + and ⋅ swapped. \(F\) is said to be self-dual if \(F = F^D\). The number of self-dual functions with \(n\) Boolean variables is
- A.
\(2^n\) - B.
\(2^{n-1}\) - C.
\(2^{2^n}\) - D.
\(2^{2^{n-1}}\)
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Correct answer: D
Correct. Partition the 2^n inputs into 2^{n-1} complementary pairs. For each pair choose the value on one input (0 or 1); self-duality forces the other to be its complement. Therefore there are 2^{2^{n-1}} self-dual functions.
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