  For applications to cryptography, it is important to represent numbers with a
small number of non-zero digits (Hamming weight) or with small absolute sum of
digits. The problem of finding representations with minimal weight has been
solved for integer bases, e.g. by the non-adjacent form in base~2. In this
paper, we consider numeration systems with respect to real bases $\beta$ which
are Pisot numbers and prove that the expansions with minimal absolute sum of
digits are recognizable by finite automata. When $\beta$ is the Golden Ratio,
the Tribonacci number or the smallest Pisot number, we determine expansions
with minimal number of digits $\pm1$ and give explicitely the finite automata
recognizing all these expansions. The average weight is lower than for the
non-adjacent form.
