A controller is provided. The controller creates a page table including page table entries including mapping information for translating a virtual address to a physical address. Each of the page table entries includes: a virtual page number, a physical frame number, valid information, and size information. The virtual page number is included in a virtual address, the physical frame number is included in a physical address, the valid information includes a first predetermined number of bits, and the size information includes a second predetermined number of bits. The first predetermined number of bits represents an address translation range in a page table entry or a number of page table entries to be grouped, and the size information represents a size indicated by each bit of the first predetermined number of bits.