  Observations and theory suggest that star clusters can form in a subvirial
(cool) state and are highly substructured. Such initial conditions have been
proposed to explain the level of mass segregation in clusters through dynamics,
and have also been successful in explaining the origin of trapezium-like
systems. In this paper we investigate, using N-body simulations, whether such a
dynamical scenario is consistent with the observed binary properties in the
Orion Nebula Cluster (ONC). We find that several different primordial binary
populations are consistent with the overall fraction and separation
distribution of visual binaries in the ONC (in the range 67 - 670 au), and that
these binary systems are heavily processed. The substructured, cool-collapse
scenario requires a primordial binary fraction approaching 100 per cent. We
find that the most important factor in processing the primordial binaries is
the initial level of substructure; a highly substructured cluster processes up
to 20 per cent more systems than a less substructured cluster because of
localised pockets of high stellar density in the substructure. Binaries are
processed in the substructure before the cluster reaches its densest phase,
suggesting that even clusters remaining in virial equilibrium or undergoing
supervirial expansion would dynamically alter their primordial binary
population. Therefore even some expanding associations may not preserve their
primordial binary population.
