Memory systems having memory devices therein with enhanced error correction capability and methods of operating same

A memory system includes a memory module having a plurality of memory devices therein. A memory controller is configured to transmit commands and addresses to the memory module in synchronization with a clock, input/output data to and from the memory module in synchronization with a data transfer clock, and perform system error correction operations on data read from the memory module. The plurality of memory devices perform on-die error correction operations, which are different from each other according to a physical location of the stored read data.