Two to one Analog to Digital conversion
Use an analogue multiplexer like the DG308 (or similar): -



It has four analogue switches and each can be digitally controlled. So, one input can feed to (say) D1 and the other input to D2. Then join together S1 and S2 and you have a change over switch that routes either signal 1 or signal 2 to the common connection of S1/S2.

Next, you use an analogue to digital converter (ADC) on the common signal.

But, you can buy plenty of ADCs combined with an input multiplexer to save you all the hassle of two chips.