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Software is any piece of code that is used to instruct the computer to do certain tasks,
Firmware is a type of software which is usually used to control the most basic function of a computer like BIOS of a PC it is a software which is usually loaded on to a single IC/Chip.
Firmware is software that is programmed into chips and usually perform basic instructions , like BIOS, for various components, Network cards, computer BIOS, etc... Software is a program that is is designed to run on a computer's operating system.