Apparatus implementing a monotonic output digital to analog converter (DAC). A high resolution monotonic DAC may be built from a lower resolution DAC using weighting functions that combine the outputs of the lower resolution DAC such that monotonicity is maintained across major carry transitions. The lower resolution DAC should have a true output and a complementary output with a half LSB bias in the output. An extended resolution DAC may be built of; cascaded low resolution DACs; a low resolution DAC in a recursive arrangement with an intermediate storage of its output; or a low resolution DAC with weighting functions that adjust at each of several major carry transition.