  Many techniques in harmonic analysis use the fact that a continuous object
can be written as a sum (or an intersection) of dyadic counterparts, as long as
those counterparts belong to an adjacent dyadic system. Here we generalize the
notion of adjacent dyadic system and explore when it occurs, leading to some
new and perhaps surprising classifications. In particular, we show that every
dyadic grid is determined by two parameters, the \emph{shift} and the
\emph{location}; moreover two dyadic grids form an adjacent dyadic system if
and only if their shifts and locations satisfy readily verifiable conditions.
