This work presents an ADC core for sensor readout applications. To achieve a high resolution combined with Nyquist-rate A/D conversion, it employs the extended counting technique (IEEE Trans. Circuits Syst. I, 42(11) (1995) 904). By making the number of counting steps programmable, the circuit allows to trade conversion speed for accuracy. In its nominal (lowest-accuracy) mode a conversion requires 71 clock cycles and achieves 16-bit performance in a conversion time of 50 ms: In the slowest, highest-accuracy mode it achieves 18-bit performance in a conversion time of 365 ms.