A memory includes cells at intersections of word lines and bit lines, word and bit line selection mechanisms and a programming mechanism. The cells on each bit line are connected in series. Cells of a word line are programmed simultaneously. For low-power reading, only some of the bit lines that intersect the word line at the programmed cells are selected and only the cells at those intersections are sensed. Another type of memory includes a physical page of cells, a sensing mechanism and a selection mechanism. Hard bits are sensed from all the cells of the physical page. Only some of those cells are selected for sensing soft bits. Another memory includes a plurality of cells, a sensing mechanism, an export mechanism and a selection mechanism. Hard and soft bits are sensed from all the cells of the plurality. Only some of the soft bits are selected for export.