How many self-dual Boolean functions of n variables are there?Please help me how to calculate such like problems.
A Boolean function $f_1^D$ is said to be the dual of another Boolean function $f_1$ if $f_1^D$ is obtained from $f_1$ by interchanging the operations $+$ and $\cdot$ and the constants $0$ and $1$. For example, if $f_1(a,b,c)=(a+b)\cdot(b+c)$ then $f_1^D(a,b,c)=a\cdot{b}+b\cdot{c}$.
A Boolean function $f$ is self-dual if $f_1=f_1^D$. Given $f_1(a,b,c)=a\bar{b}+\bar{b}c+x$, find the Boolean expression $x$ such that $f_1$ is self-dual.
How to calculate this value?Please help me.
Best Answer
The total number of self dual functions possible with $n$ variables is $2^m$, where $m=2^{n-1}$.