1. An integrated circuit (“IC”) comprising: a configurable circuit for configurably performing one of a plurality of operations based on configuration data; a plurality of configuration storage circuits for storing a plurality of configuration data sets for the configurable circuit; and an interconnect circuit for switchably connecting the configurable circuit to different sets of the configuration storage circuits to receive different configuration data sets, said interconnect circuit comprising (i) a set of clocked storage circuits and (ii) a set of unclocked storage circuits for temporarily storing the received configuration data sets.