A data storage device according to example embodiments of inventive concepts includes a nonvolatile memory and a memory controller. In the nonvolatile memory, one read unit is configured to store a plurality of codewords. If a fail occurs in one or more codewords stored in the nonvolatile memory, the memory controller may search a read voltage of the nonvolatile memory using a correctable codeword. The data storage device according to example embodiments may predict an optimum read voltage level without performing a valley search operation.