A two-step SAR ADC with a highly programmable transfer function is presented, extending the application domain of non-linear conversion from signal-specific scenarios to a wider range of data-constrained and information-aware applications. By utilizing a thermometer-encoded programmable capacitive DAC for coarse quantization, the converter can be reconfigured to achieve arbitrary piecewise-linear (PWL) transfer functions, and is not restricted to exponential and logarithmic conversion typical of non-linear ADCs. Analysis of the thermometer DAC design is provided to explore the trade-offs between flexibility, gained resolution, and resource overhead. A 7-bit prototype fabricated in 180nm CMOS validates the presented architecture; multiple measured linear and non-linear transfer functions showcase the flexibility of the reconfigurable PWL-ADC. The approach enables variable effective resolution across the full-scale range, providing up to 9.5-bit performance using a 7-bit ADC. Measurements using an ECG waveform are used to further highlight application-specific advantages enabled by the PWL-ADC.