1. A method of obtaining diagnostic information from a logic device comprising logic circuits and a built-in self-test system (BIST) comprising scan chains, the method comprising: using the scan chains, applying a stimulus vector to the logic circuits, capturing responses of the logic circuits to the stimulus vector and shifting the captured responses towards the outputs of the scan chains; generating a representative signature representing responses output by the scan chains; concurrently with the generating, temporarily storing the responses output by the scan chains such no more than a most-recently output subset of the responses is stored, the subset consisting of fewer than all of the responses generated in response to the stimulus vector; determining whether the representative signature is a fault-indicating representative signature; and when the representative signature is a fault-indicating representative signature, outputting at least some of the stored responses.