What is the highest theoretical possible resolution of the IBM VGA (Clock 28MHz, any framerate, monochrome mode, 256K RAM)?
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If you only consider the RAM. and what you can fit into 256KB in monochrome mode:
256 * 1024 = 262,144 bytes of video memory
1 byte of video memory = 8 monochrome pixels
256KB RAM = 262,144 bytes * 8 pixels = 2,097,152 pixels (approx two megapixels)
2048x1024 resolution = 2048 * 1024 = 2,097,152 pixels
Therefore 2048x1024 is one possible resolution that would use every last bit of video memory, in monochrome mode. Another mode which would leave a few bytes unused is 1920x1080, so you could fit a B&W 1080p picture in 256KB of video RAM.
Of course the actual resolution you can get would probably be much lower due to the clock. I'm not sure how it works and whether you could lower the refresh rate enough to get say 1080p within range, so someone else will probably answer that. Chances are even if it's possible, the refresh rate would be too low for a normal monitor to sync to the signal, so you may not be able to see the picture even if it could be generated.
But this does at least put an upper limit on the resolution you can get.
Maximum resolution, if you want to display it on a standard VGA monitor, is 720x480.
Highest possible values that fit into registers, that of course can be emulated, but no real monitor would display it.
Vertical total scanlines is 10 bits, and there is at least one bit to count every other scan line, so that effectively doubles the amount.
Horizontal total (character clocks) is 8 bits, and there could be also bits to divide the clock down to get longer scan lines.
But no real monitor would ever of course display such resolutions (2048*2048, at 6.75 Hz refresh rate..)
Highest possible horizontal resolution is 2304, as characters can be 9 pixels wide. Still can't display it on anything though.
True, it is possible in text mode, graphics modes being limited to 8. In fact, the register holds total h characters minus 5, so up to 260 characters could be possible. Maybe one more, if 0 is regarded as 256 instead of 0. Of course the active video area is a bit less, as some space may be necessary to reserve for blanking and syncs.
