**Problem:** Determine whether it is possible to find a cube and a plane such that the distances from the vertices of the cube to the plane are $0,1,2,3,....,7.$

Now in the solution, the author states that: 

> 
> If we consider a cube of edge length $1$ unit with the coordinates
>  $(0,0,0),(0,0,1),(0,1,0),(0,1,1),(1,0,0),(1,0,1),(1,1,0)$ and
>  $(1,1,1)$ we observe that these are binary representations of the
>  numbers $0,1,2,3...,7.$ This motivates us to consider the plane
>  $x+2y+4z=0.$
> 
> 
> 

I didn't get how the observation of coordinates being binary equivalents of the numbers $0,1,2..,7$ motivate the author to consider the plane $x+2y+4z=0.$ Please explain.