  We examine the dynamical destruction of binary systems in star clusters of
different densities. We find that at high densities (10^4 - 10^5 Msun pc^-3)
almost all binaries with separations > 10^3 AU are destroyed after a few
crossing times. At low densities (order(10^2) Msun pc^-3) many binaries with
separations > 10^3 AU are destroyed, and no binaries with separations > 10^4 AU
survive after a few crossing times. Therefore the binary separations in
clusters can be used as a tracer of the dynamical age and past density of a
cluster.
  We argue that the central region of the Orion Nebula Cluster was around 100
times denser in the past with a half-mass radius of only 0.1 - 0.2 pc as (a) it
is expanding, (b) it has very few binaries with separations > 10^3 AU, and (c)
it is well-mixed and therefore dynamically old.
  We also examine the origin of the field binary population. Binaries with
separations < 10^2 AU are not significantly modified in any cluster, therefore
at these separations the field reflects the sum of all star formation. Binaries
with separations in the range 10^2 - 10^4 AU are progressively more and more
heavily affected by dynamical disruption in increasingly dense clusters. If
most star formation is clustered, these binaries must be over-produced relative
to the field. Finally, no binary with a separation > 10^4 AU can survive in any
cluster and so must be produced by isolated star formation, but only if all
isolated star formation produces extremely wide binaries.
