--- HD 101 ---
First of all, saying that a display is 720p or 768p (or even 1080p) is only part of the "picture". The horizontal resolution is the other part. A "correct

" 720p HD display is 1280 x 720 pixels, and a 1080p HD display is 1920 x 1080 pixels (digital displays only).
A 1024 x 768 image or display is not a true HD format, it is a PC format. To make a 1024 x768 panel into a 16:9 format requires that the pixels have to be non-square (they're stretched horizontally). These are typically known as ED (extended definition) displays.
A lot of manufacturers (like my Olevia and LG LCD flat panel displays) use a 1366 x 768 pixel panel. I believe (but have no proof - just an engineering guess) the reason is that these units are designed to be used with PCs as well as with true HD signals

. They chose to use 1366 x 768 (instead of "the more correct" 1280 x 720) because the slight extra cost associated with the slightly larger array (and the attendent extra scaling required) is less than that needed to easily interface with PCs (via their VGA input). The closest PC video card formats fit the 768 vertical resolution (either 1024 x 768 or, roughly, 1366 x 768) for 1:1 PC signal mapping.
A lot of manufacturers have taken flack for not being able to do 1:1 from a PC for video games. Using a 1366 x 768 panel eliminates the problem without a lot of push-ups on their part (and in the PC display cards). With the current state-of-the-art one chip scaler circuits, scaling a video input from 1280 x 720 to 1366 x 768 is no big deal. And this scaling has very little, observable, effect on the quality (artifacts, sharpness, etc.) of the resulting picture (from my observations).
My PJ, on the other hand, has 1280 x 720 panel(s). However, it also does not do a 1:1 pixel mapping form a PC very well (some loss of sharpness due to the PC's software scaling). This is (I believe) the same reasoning as to why the new, low cost, DLP PJs went with 768 (vertical resolution) panels.
Conversion from a 1080i HD signal, for either 1280 x 720 or 1366 x 768 panels, is another subject entirely. This process is not always done correctly (some hardware converts each 1920 x 540 field - 2 fields make up a 1920 x 1080 frame) and de-interlace that to 540p images

. Then they convert the 540p images to 720p frames (which loses the full 720p resolution). If done correctly, the 1080i should be de-interlaced to 1080p and then down-rezzed to either 720p or 768p (depending on the display's native resolution).
--- End of Lecture ---

We now return you to your regular programming

.