Firmware is a type of very basic software that's usually preinstalled on a device from factory and serves to provide the most essential functionality of the device. On simple devices, like mp3 players or remote controls, firmware may be all that's ever needed for the device's functioning, while on more complex ones, such as personal computers, firmware (e.g. BIOS or UEFI) allows basic configuration and installation of more complex software (such as an operating system) and possibly provides functions that the installed software can use. Firmware is normally not meant to be rewritten by the user and is installed in some kind of memory that's not very easy to rewrite, it may even be hard-wired in which case it becomes something on the very boundary of software and hardware.
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