Wearable wireless biomedical sensors will play important roles in future prevention-oriented healthcare. The strictly restricted power budget for the wearables rendered Nyquist sampling scheme unsuitable for this type of sensors. This is because the Nyquist sampling does not make use of the sparse characteristics of biomedical signal. In this paper we presented an alternative sampling scheme, called event-driven sampling, which takes advantage of sparsity in the biomedical signal and generates considerable fewer sampling points compared to Nyquist sampling scheme. Traditionally, event-driven ADC uses two comparators to generate outputs, which limits the minimum power of the ADC. We propose a new ADC structure that utilizes only one high-resolution comparator to generate output while a low-resolution comparator determines the direction of input. In this way, the minimum power of a level-crossing ADC can be reduced almost half compared to traditional level-crossing ADC.