I borrowed a few images to help show how this works:
Notice the two gold connectors on the top of the video card. When you have two cards installed in a computer, you'll take two of the Crossfire bridges (one is included with each card) and connect each between the two cards, connecting to the gold connectors. This allows the cards to communicate with each other with each Crossfire connector providing a link between the two cards. The cards use these links for communicating with each other, working out which card will display what part of the image. As I understand it, the most common way is called 'Alternate Frame Rendering'. This means that the first card will render all the even numbered video frames, and the second card renders the odd numbered video frames. This can be scaled to three or even four cards, but the performance doesn't tend to justify the additional cost of more than two cards IMO.
I sold my old GTX 260s to buy these cards, so the overall cost of upgrading wasn't that high. 30" monitors are nice, but too damn expensive!

It would be a real challenge to squeeze a second monitor of that size on my desk anyway.
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