We consider spectrum sensing in a wideband cognitive radio system where 1-bit analog-to-digital converters (ADCs) are adopted at the radio frequency (RF) sensors. We focus on a practical scenario where multiple narrow-band radio systems coexist in the considered wide spectrum range and the RF sensor has no prior knowledge about those ambient radio systems. First, we use Van Vleck's arcsine law to analyze the impact of 1-bit sampling on performance of covariance matrix reconstruction. Second, we propose a novel 1-bit wideband spectrum sensing algorithm based on the subspace technique. We show that the proposed method exhibits near-zero false alarm (FA) while achieves the similar probability of detection (PD) performance as compared to conventional FFT-based and correlation-based wideband sensing methods.