How do binary separations depend on cloud initial conditions?

We explore the consequences of a star formation scenario in which the isothermal collapse of a rotating, star-forming core is followed by prompt fragmentation into a cluster containing a small number (Nless than or similar to10) of protostars and/or substellar objects. The subsequent evolution of the cluster is assumed to be dominated by dynamical interactions among cluster members, and this establishes the final properties of the binary and multiple systems. The characteristic scale of the fragmenting core is determined by the cloud initial conditions (such as temperature, angular momentum and mass), and we are able to relate the separation distributions of the final binary population to the properties of the star-forming core. Because the fragmentation scale immediately after the isothermal collapse is typically a factor of 3-10 too large, we conjecture that fragmentation into small clusters followed by dynamical evolution is required to account for the observed binary separation distributions. Differences in the environmental properties of the cores are expected to imprint differences on the characteristic dimensions of the binary systems they form. Recent observations of hierarchical systems, differences in binary characteristics among star forming regions and systematic variations in binary properties with primary mass can be interpreted in the context of this scenario.