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Baron said:

That's not entirely accurate. Nowadays there are plenty PC games that use (almost) 6 GB of RAM. Battlefield 3 on 1080p @ Ultra settings for instance will utilize 6 or more GB's of RAM.

The difference between PC's and consoles is the heavy OS and the dozens of processes running in the background while playing a game. Where Windows 7 requires 1 GB of RAM minimum (the 64 bit version requires 2 GB's even) a console OS uses a lot less. I reckon 512 MB of system memory is more than sufficient for any console.

What is most important with consoles is video memory. At the time of the 360's launch, normal graphics cards had 256 MB of memory and the high end ones had 512 MB. That's why the 360 and PS3 also had 512. That's what was deemed sufficient for any game. Off course back then the most common gaming resolution was 1024x768. Now the most common gaming resolution is 1080p. 2.6 times larger than 1024x768. The result of that can be seen with today's GPU's. Budget cards are equipped with 1 GB and high end cards feature 2 or even 3 GB's of RAM. With that in mind and the performance of the 360 and PS3 @ their launch in mind I think we can say that a console with 1 or 1.5 GB's of video memory, like the Wii U is rumored to have, will be sufficient for 1080p gaming.

I expect the next XBox and Playstation to have between 2 and 4 GB's of video memory as I expect the next series of graphics cards will also have that amount of RAM.

The output resolution has only had a significant impact on the graphics card's memory in the early days of 3D graphics cards ...

1080p is (roughly) 2 million pixels and even with a 32bit buffer each screen buffer you use is only going to take up (roughly) 8MB of memory. Between double buffering, a Z-Buffer, and (potentially) other buffers for effects it is likely that a game displaying at 1080p is using between 32MB and 64MB of memory for buffering; which represents less than 5% of memory in these new graphics cards.

From my (very limited) understanding, the bulk of graphics card memory is used up by the graphics card caching and buffering models and textures because of the cost associated with reading these assets from the "slow" memory and transferring this data across the PCI-e bus. Since consoles tend to use a unified memory architecture that is made up of the higher speed GDDR memory there are significant reductions in the need for caching. This is one of many reasons why a console doesn't require as much memory as a similar PC.