To provide a data processing system that includes a nonvolatile memory device capable of storing multilevel data and enables increasing storage capacity of a main memory device when the data processing system is activated. The data processing system includes an arithmetic processing device, a main memory device, and a nonvolatile memory device. The main memory device includes a volatile memory device, and the nonvolatile memory device is configured to store multilevel data in one memory cell. When the data processing system is deactivated, the nonvolatile memory device stores binary data, whereby the stored data can be held for a long time. Upon activation, the nonvolatile memory device stores multilevel data, whereby increasing storage capacity. When the storage capacity is increased, a free space is generated in the nonvolatile memory device, which can be used as a part of the main memory device of the data processing system.