An embodiment of the present invention is a technique to design a DAC. A double-summed-to-zero (DSTZ) graph is created having a plurality of nodes linked by a plurality of directed branches. The DSTZ graph represents a finite state machine (FSM) that generates a sequence for a switching block used in a mismatch-shaping digital-to-analog converter (DAC). Each of the plurality of nodes represents a state in the FSM. The DSTZ graph has a total work function and a total potential energy summing to zero for a cycle traversal. A switching sequence is generated starting from a reference node in the plurality of nodes in response to an input sequence. The reference node has a zero potential energy.