1. An integrated circuit (“IC”) comprising: a) a set of memory cells for storing configuration data for configuring configurable circuits of the IC; b) a set of non-configurable memories for storing and outputting non-configuration, user-design data; c) a set of volatile configurable logic circuits, each volatile configurable logic circuit for configurably performing one of a set of functions based on configuration data received by the volatile configurable logic circuit; d) a set of volatile configurable interconnect circuits for configurably routing signals between the volatile configurable logic circuits; and e) a set of multiplexers, each multiplexer comprising input, output, and select terminal sets, (i) wherein at least a particular multiplexer's input terminal set is for receiving an output of a particular non-configurable memory from a subset of the volatile configurable interconnect circuits, wherein said particular non-configurable memory comprises a two-dimensional array of storage elements, and (ii) wherein at least the particular multiplexer's select terminal set is for receiving a set of output of a subset of the volatile configurable logic circuits, wherein said received output of the subset of the volatile configurable logic circuits directs the particular multiplexer to output only a portion of said output of the particular non-configurable memory that is received at said input terminal set along the particular multiplexer's output terminal set.