ram

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In 16 bit mode you are using 2 bytes per pixel.
To display a full screen would be 800x600x2=960,000.
Duble buffering would be twice that or 1,920,000
In 24 bit mode you are using 3 bytes per pixel
and in 32 bit mode you are using 4 bytes per pixel.
A 1024 x 768 32 bit full screen would use: 1024x768x4=3,145,728 bytes per screen and dubble buffering would use twice as much.
That's the math, for the display itself, impossible to be less. Other video features could increase this though.

In answer to your question about the large memory used.
DirectX stores textures and 3D objects in video memory for quicker rendering. It is much faster to move data from one area of video memory to another than from computer memory to video memory. Some video memories run at 800 mhz while most computer memories still run at less then 200 mhz.
To lower your video memory useage you must lower the number of textures or objects you are loading at once. Only load what you need when you need it.

When dealing with textures the same math as above applies.
A 512x512 32 bit texture uses 1,048,576 bytes, of your video memory to store it there for use.
One common mistake people make is they look at a jpg that is 150k long and think it only uses 150k, but jpg's are highly compressed files, and are expanded by your computer when they are loaded.
So that 150k jpg could easily use 2 megs of memory when loaded.
To lower your memory useage you could use 256x256 16 bit textures which only use 131,072 bytes per texture when loaded.
That's only 1/8 as much. as the 512x512 32 bit.

I hope this helps explain the large memory useage question.