  Chirality is ubiquitous in nature and chiral objects in condensed matter are
often excited states protected by system's topology. The use of chiral
topological excitations to carry information has been demonstrated, where the
information is robust against external perturbations. For instance, reading,
writing, and transfer of binary information are demonstrated with chiral
topological excitations in magnetic systems, skyrmions, for spintronic devices.
However, the next step, the logic or algebraic operation of such topological
bits has not been realized yet. Here, we show experimentally the switching
between solitons of different chirality in a one-dimensional electronic system
with $Z_4$ topological symmetry. We found that a fast-moving achiral soliton
merges with chiral solitons to switch their handedness. This corresponds to the
realization of algebraic operation of $Z_4$ topological numbers. Chiral
solitons could be exploited for storage and operation of robust topological
multi-digit information.

Mesoscale and Nanoscale Physics;Pattern Formation and Solitons;Exactly Solvable and Integrable Systems