Arrange $16$ bit binary digits into a circle

54 Views Asked by At

How to arrange $16$ binary digits into a circle, such that the $16$ 4-bit binary numbers will only be present once?

1

There are 1 best solutions below

1
On BEST ANSWER

Create a directed graph where the nodes are all of the 3-bit binary numbers and an arc goes from a vertex labeled $abc$ to a vertex labeled $xyz$ if $b=x$ and $c=y$. Label that arc $z$.

enter image description here

This directed graph is strongly connected and every node in this directed graph has the same indegree and outdegree. Therefore, there is a directed Euler circuit in this directed graph. Every such circuit corresponds to a De Bruijn sequence in a pretty obvious way.