  We extend the well-known Dumont--Thomas numeration system to $\mathbb{Z}$ by
considering two-sided periodic points of a substitution, thus allowing us to
represent any integer in $\mathbb{Z}$ by a finite word (starting with
$\mathtt{0}$ when nonnegative and with $\mathtt{1}$ when negative). We show
that an automaton returns the letter at position $n\in\mathbb{Z}$ of the
periodic point when fed with the representation of $n$. The numeration system
naturally extends to $\mathbb{Z}^d$. We give an equivalent characterization of
the numeration system in terms of a total order on a regular language. Lastly,
using particular periodic points, we recover the well-known two's complement
numeration system and the Fibonacci analogue of the two's complement numeration
system.

Combinatorics;Dynamical Systems;Number Theory