A memory includes a plurality of columns and a redundant column. The memory includes a plurality of multiplexers corresponding to the plurality of columns. Depending upon the location of a defect, the multiplexers are configured to select for their corresponding column or an immediately-subsequent column to their corresponding column.

A method of operating a nonvolatile memory device includes performing a first memory operation on a first memory block of a plurality of memory blocks and a curing operation on a portion of the first memory block when a status signal indicates a ready state of the nonvolatile memory device during an interval equal to or greater than a reference interval after the first memory operation is completed. The nonvolatile memory device includes the plurality of memory blocks, each memory block including a plurality of vertical strings extending in a vertical direction with respect to a substrate.

A semiconductor memory device includes a memory string having first and second selective transistors, each of which includes a charge storage layer and a control gate, a back gate transistor which includes a charge storage layer and a control gate, and memory cell transistors connected to each other and to the back gate transistor in series between the first and second selective transistors. In case any of the memory cell transistors is defective, the defect is indicated by storing a charge in the charge storage layer of at least one of the first and second selective transistors and the back gate transistor.

A memory system may include a memory module comprising a plurality of memory chips mounted therein each memory chip comprising a plurality of banks, the memory chips being simultaneously accessible based on the same command and address; and a memory controller suitable for mapping the banks of the memory chips to each other while rearranging an order of the banks of each of the memory chips based on repair information of the memory chips.

A method of operating a nonvolatile memory device includes performing a first memory operation on a first memory block of a plurality of memory blocks and a curing operation on a portion of the first memory block when a status signal indicates a ready state of the nonvolatile memory device during an interval equal to or greater than a reference interval after the first memory operation is completed. The nonvolatile memory device includes the plurality of memory blocks, each memory block including a plurality of vertical strings extending in a vertical direction with respect to a substrate.

An image sensor includes a pixel array and a peripheral circuit. The peripheral circuit is electrically connected to the pixel array and includes a logic block and at least one redundancy block to replace the logic block when the logic block is a defective block.

A system includes a processor and a memory. The processor locates a first memory chip that is faulty in a memory. After the first memory chip is isolated or replaced, the processor may reset the first memory chip when other memory chips in the memory are maintained to work normally. When a fault occurs in a memory chip in the memory, after the first memory chip that is faulty is isolated or replaced, the processor may independently reset the first memory chip without affecting the other memory chips in the memory. Resetting the first memory chip enables the first memory chip to restore to normal. A memory chip that can be normally used is used as a redundant memory chip or may continue to be used.

A memory system and a data processing system including the memory system may manage a plurality of memory devices. For example, the data processing system may categorize and analyze error information from the memory devices, acquire characteristic data from the memory devices and set operation modes of the memory devices based on the characteristic data, allocate the memory devices to a host workload, detect a defective memory device among the memory devices and efficiently recover the defective memory device.