Memory system storing multi-bit data, program method thereof, and computing system including the same

A computing system including the memory system is provided to prevent data loss due to the power fail when the low data bit is operated in the program operation of the superior data bit through data backup operation. A method for programming multi-bit flash memory device includes memory cells storing multi-bit data is comprised of steps of: determining whether data stored in the selected memory cell are lowest data or not(B320); performing backups LSB stored in the selected memory cell if the data to be stored in the selected memory cell is not LSB(B330).