In a printer of the present invention, an EEPROM that carries out sequential access and has a relatively small storage capacity is applied for storage elements mounted on both black and color ink cartridges, which are detachably attached to the printer. Pieces of information relating to each ink cartridge, for example, pieces of information on remaining quantities of respective inks in the ink cartridge, are stored in the storage element of the ink cartridge. A format of addressing adopted in the storage elements of the ink cartridges is different from that adopted in an EEPROM incorporated in a printer main body of the printer. A control IC provided in the printer accordingly converts the storage format of addressing, before writing the information into the storage elements of the ink cartridges. In the printer, a RAM is mounted with the control IC on a carriage, and the pieces of information to be written into the storage elements of the ink cartridges are temporarily registered in the RAM. The pieces of information are then written into the respective storage elements of the black and color ink cartridges, for example, at a timing of a power-off operation. The signal lines and the memory used in the course of writing the information into the storage elements are identical with the signal lines, through which print data are transmitted to a print head mounted on the carriage of the printer, and the memory, in which the print data are stored. The arrangement of the present invention reduces the manufacturing cost of the ink cartridge and also enables size reduction of the whole printer.