The dac consists of a resistor ladder, switches, ground and Vref wires. The resistors in series ("spine") are valued "R" and the rungs have value 2R. The low terminal on the run resistor can be switched between Vref and gnd. The span of voltages at the output ranges from Vref to 0V (gnd). The ladder spine is terminated in a resistor of value 2R to gnd, so that the impedance is the same at each node of the ladder. The further each rung is from the output, the smaller it's effect. The effect of each rung is Vref/s^n, where n is the number of positions away from the output. To analyze the dac, cut it infront of each rung. The "tail" will always have thevenin resistor R, and the voltage will be the weighted sum of all the rungs behind that point.