A system includes a capacitance adjustment module and a control module. The capacitance adjustment module is configured to connect one or more of N capacitors in parallel with one of a first and second capacitance. The control module identifies the smaller of the first and second capacitances and identifies the larger of the first and second capacitances. Subsequently, the control module, during each of M iterations, instructs the capacitance adjustment module to connect at least one of the N capacitors across a set of nodes in parallel with the smaller identified capacitance, and determines whether the capacitance associated with the set of nodes is greater than the larger identified capacitance. After the M iterations, the control module approximates the difference between the first and second capacitances based on which of the N capacitors are connected across the nodes. M and N are integers greater than or equal to 1.