The component in an audio card that is doing this is called a DAC which stands for Digital to Analog Converter. There are a few different designs for these devices depending on the quality, efficiency and cost. A simple to explain and quite common DAC connect the input bits to transistors in the circuit which enables or disables resistors, current sources or capacitors depending on the value of that bit. All of the activated components will then sum together to create a voltage of the correct value on the output.
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