Butterfly permutation
This permutation is getting by interchanging the important significant bit in address with smallest significant bit.
Ex. X_{n-1}, X_{n-2}, and X_{1}.X_{0} = X_{0} X_{n-2 }....... X_{1} X_{n-1}
001↔100, 010↔010
011↔110,
An interconnection network stand on this permutation is the butterfly network. A butterfly network is called a blocking network and it does not permit an arbitrary connection of N inputs to N outputs without clash. The butterfly network is customized in Benz network. The Benz network is said to be non-blocking network and it is produced by joining two butterfly networks back to back, in such a way that data flows forward through one and in reverse through the other.