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Modern GPUs do not have analog VGA output on their DVI connector and won't work with passive DVI-to-VGA adapters. You need an active adapter which has analog-to-digital converters inside.
Minor point but it's actually a DAC (Digital-to-Analog) in this case not an ADC chip.
And just FYI for whoever may care, in past cards the digital output of DVI was usually tapped off internally, sent through a DAC, then either sent as VGA direct or a separate set of pins in DVI-I (meaning "integrated" DVI and VGA pins).
The "VGA adapter" would be passive because the set of pins for analog would connect directly to it. Using DVI would connect to the digital pins.
The removed this DAC as it adds slightly to the cost of the card (as the DVI-I connector would too). Probably not much, but very few people have VGA-only monitors.
So a DAC just adds back the digital-to-analog converter functionality. VGA was originally only needed for CRT's to directly drive the horizontal, vertical and brightness by changing the appropriate voltages.
VGA inputs on flat panels is for compatibility with VGA outputs if you have no supported digital output, but if you had that the GPU is outputting digital, then going through a DAC, then the analog signal goes into the flat-screen's VGA input and converted back to digital via an ADC.