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 X₁.X₀ = X₀   X_n-2 ....... X₁   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.