I never thought of Windows 3.1 as an OS. The other 2 was MS-DOS and Windows 95.
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Though Windows 95 was arguably similar running atop “DOS 7” it actually imposes its own 32-bit environment with its own “protected mode” drivers once booted. Dropping to DOS reverted to “real mode”.
What that did is use DOS as a first stage boot loader, then switched into protected mode and created a v86 task which took over the state of DOS. The protected mode code than finished booting.
v86 mode was a mode for creating a virtual machine that looked like it was running on a real mode 8086 but was actually running in a virtual address space using the 80386 paging VM system.
When you ran DOS programs they ran in v86 mode. If a DOS program tried to make a BIOS call it was trapped and handled by the 32-bit protected mode code.
v86 mode tasks could be given the ability to directly issue I/O instructions to designated devices, so if you had a device that didn't have a 32-bit protected mode driver a DOS driver in a v86 task could be used.
For devices that did have a 32-bit protected mode they would not give v86 mode direct access. Instead they would trap on direct access attempts and handle those in 32-bit protected mode code.
I wish Linux had adopted a similar use of v86 mode. I spent a while on some Linux development mailing list trying to convince them to add a simplified version of that. Just virtualize the BIOS in a v86 task, and if you've got a disk that you don't have a native driver use that v86 virtualized BIOS to access the disk.
Eventually someone (I think it may have been Linus himself) told me to shut up and write the code if I wanted it.
My answer was I couldn't do that because none of my PCs could run Linux because there were no Linux drivers for my SCSI host adaptors. I wanted the feature so that I could run Linux in order to write drivers for my host adaptors.
OS/2 did the v86 virtualized BIOS thing, and that was how I was able to write OS/2 drivers for my SCSI host adaptors.