For high resolution resistor string DACs, a resistor string is placed in an array of columns and rows, each resistor tap is connected to a switch network, and a decoder is used to select switches to be closed such that sub-DAC voltage comes from the resistor taps connected to the selected switches. The voltages from each row of the resistor string are fed into a multiplexer, wherein the multiplexer produces an output voltage. A method and apparatus are disclosed for implementing the reflective nature of Gray code to design a DAC such that all the switches in a column of the resistor string may be controlled with only one control signal, thereby reducing extra routing costs, surface area, and dynamic power consumed by the circuit.