For example, if i make a very simple bootloader that runs a “hello world” program (as the operating system), where is the graphical representation of the text processed. The the GPU render the text, or the the hardware. Is basic text input and output hard-coded in either the BIOS or processor, or is it integrated in assembly/programming langauge?
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The GPU can be in the processor or in the discrete card or even the motherboard. Basic I/O is done via the framebuffer in whatever handles it and is memory mapped by the BIOS usually to 0xb8000. To get simple I/O you just write the ascii characters to the framebuffer and the card will just output them to the screen (in a basic OS like you said).
It can be accomplished in any low level language that allows you to directly address memory values and can be compiled into native code.
For text you see on your screen (like this text) that’s typically software’s job as there are fonts, styles and other things to deal with. This is usually handled via basic API’s exported by the operating system that allow screen drawing or by the drivers themselves.