There's a small 8 KB BIOS ROM fitted on the motherboard that gets executed whenever the console is powered on. The program itself does not qualify as an 'Operating System'; it is more accurately described as a Boot Manager.
Medium selector
The main goal of the BIOS is to bootstrap a valid game (from either game slot) in the following order of priority: the Sega Card, the cartridge, and the expansion module.
The boot process works as follows:
- The console is switched on.
- The BIOS copies part of its code to main RAM.
- This is a crucial step, since the program will start manipulating I/O ports, which will eventually disable access to the ROM!
- Show the splash screen (only in USA/Europe models).
- Check each slot for a valid game.
- This is done by talking to the I/O controller chip to activate the required slot. Then, the boot program copies the game header (16 bytes) from each slot to check if the game content is valid (thus, properly inserted). The header must have
TMR SEGAencoded.
- This is done by talking to the I/O controller chip to activate the required slot. Then, the boot program copies the game header (16 bytes) from each slot to check if the game content is valid (thus, properly inserted). The header must have
- Perform the region check.
- Redirect execution to the game.
Surprise screen
If any of the checks fail, the console loops indefinitely while showing a screen that prompts the user to insert a valid game.

Video - USA/Europe error message (after the initial splash).

Video - Japanese 'error' message (enhanced by the FM chip!).
I have to say, in terms of the design of the error screen, the creative differences between regions are quite significant. The first time I heard the colourful Japanese version, I thought it was based on Electric Light Orchestra (the band), but it is actually from Space Harrier (the game). Also, the perspective effect on the floor is accomplished by altering the colour palettes.
More regional differences
Because the Japanese variant was backwards compatible with the SG-1000, the header check is replaced with an 'integrity check' that instead reads data from the first 256 bytes multiple times to detect if it is garbage.
Furthermore, the Mark III doesn't have a BIOS, so the slots are activated with hardware switches. Furthermore, the cartridge is the medium with the highest priority.
Updatability and later BIOS chips
The BIOS ROM, by its nature, is not updatable. Although, as new console revisions entered the market, it was discovered that Sega also updated the BIOS program.
Later ROMs even embedded entire games! As a consequence, the chip got bigger and was accompanied by a dedicated mapper.