According to one embodiment, a semiconductor memory includes a first memory cell array including a plurality of first memory cells; and a second memory cell array including a plurality of second memory cells. Each of threshold voltages of the first memory cells and the second memory cells is set to any of a first threshold voltage, a second threshold voltage higher than the first threshold voltage, and a third threshold voltage higher than the second threshold voltage. Data of three or more bits including a first bit, a second bit, and a third bit is stored using a combination of a threshold voltage of the first memory cell and a threshold voltage of the second memory cell.