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How does it work?

No more multiplexers

One of the most important aspects of Optimus is that it doesn't rely on any additional hardware beyond what's in the GPU itself. This is important because, in previous iterations, multiplexers (aka muxes) were required to regulate which GPU the system should use to display the image on the screen. Indeed, as the slide below demonstrates, several 'muxes' were required to make this work, incurring greater cost of manufacturing, as well as more power drawn for each extra component.
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Lots of multiplexers increase the complexity, cost and power draw of the system board.

Ultimately this meant that having switchable graphics in a laptop made it more expensive, since any system utilising it had to have its own unique system board design. Given, as nVidia discovered, so few people actually used the feature anyway, it's little wonder so few graphics-switching laptops have made it to retail despite the technology being available for several years.

No more custom APIs

Another challenge in the old system was software. Due to operating systems only allowing for one graphics driver to be present, nVidia and Intel had to cooperate to produce a single driver and nVidia had to develop what it calls a Display Driver Interposer that could see the two drivers and work with them.
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Windows 7 allows more than one display driver to be present at the same time.

It's Microsoft that takes the credit here, however, as Windows 7 can now operate with two display drivers present, negating the need for a unified driver or the Display Driver Interposer. Thus you can use the standard graphics drivers for both, which also means you can always use the latest driver rather than wait for Intel and nVidia to put their unified driver out. Consequently, Windows 7 is one of the requirements for Optimus.

Optimus Copy Engine

This is where things get really clever. What really makes Optimus work is a piece of tech inside the GPU itself: the Copy Engine. It is this that allows nVidia to eliminate muxes and thus make implementing 'switchable' graphics a whole lot easier and cheaper.
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The Optimus Copy Engine means the discrete GPU doesn't need to be connected to the display.

How? By passing all responsibility for displaying a frame on your display to the integrated graphics. Once a frame has been rendered by the discrete GPU, the copy engine sends it to the system memory (RAM), which in turn sends it to the integrated graphics that displays the frame on-screen. Fundamentally it means the nVidia GPU has no actual connection to the display, thus negating the need for a multiplexer to make the switch.

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