A two-terminal memory array includes a plurality of first and second conductive traces. An address unit operatively applies a select voltage across a selected pair of the first and second conductive traces and applies a non-select voltage potential to unselected traces. A total current flowing in the selected first conductive trace and a leakage current flowing through unselected second conductive traces are sensed by a sense unit in a one cycle or a two cycle pre-read operation. The total and leakage currents can be combined with a reference signal to derive a data signal indicative of one of a plurality of conductivity profiles that represent stored data. The conductivity profiles can be stored in a resistive state memory element that is electrically in series with the selected first and second conductive traces.