DAC Ladder Networks
How can we understand ladders? A step at a time. In all cases, we'll have some reference voltage Vref that is the full scale range of the DAC. For purposes of this section, presume that the DAC encodes straight binary from 0 to Vref. Other coding schemes aren't hard to understand once this first one is clear.
The first circuit to consider is a simple voltage divider. For two equal resistors, we have 3 points we can monitor: zero, the mid-point of the resistive ladder (where V = Vin/2), and the top of the ladder (where V = Vin). If we had an electronic switch, we could choose among 3 outputs. Clearly, given N resistors, we can select among N+1 outputs.