Aside from comparators, the most important analog part of a dual slope ADC is an integrator. The circuit is:

V_{out} is the integral of V_{in}, or actually

Any time one wants to reset the integral to 0, one simply shorts the capacitor. Notice the negative sign -- positive input voltages give negative output voltages.

If we want to digitize a postive voltage, we'll also need a reference voltage that's negative (and, of course, if we want to digitize negative voltages, we need a positive reference). We integrate the unknown voltage V_{in}(t) for a fixed time T. For now, let's assume the potential is constant in time. The integral will be -V_{in}T/RC. Now disconnect the input potential. Since the input is 0, the integral holds constant. Next, connect the input to the reference voltage (opposite sign to V_{in}) and integrate. What will happen? The integrator will ramp towards 0. How will we know when we get to zero? Multiple choice, choose the right component: