In this paper, we propose binary sparse convolutional networks called BSC-Net for efficient point cloud analysis. We empirically observe that sparse convolution operation causes larger quantization errors than standard convolution. However, conventional network quantization methods directly binarize the weights and activations in sparse convolution, resulting in performance drop due to the significant quantization loss. On the contrary, we search the optimal subset of convolution operation that activates the sparse convolution at various locations for quantization error alleviation, and the performance gap between real-valued and binary sparse convolutional networks is closed without complexity overhead. Specifically, we first present the shifted sparse convolution that fuses the information in the receptive field for the active sites that match the pre-defined positions. Then we employ the differentiable search strategies to discover the optimal opsitions for active site matching in the shifted sparse convolution, and the quantization errors are significantly alleviated for efficient point cloud analysis. For fair evaluation of the proposed method, we empirically select the recently advances that are beneficial for sparse convolution network binarization to construct a strong baseline. The experimental results on ScanNet and NYU Depth v2 show that our BSC-Net achieves significant improvement upon our srtong baseline and outperforms the state-of-the-art network binarization methods by a remarkable margin without additional computation overhead for binarizing sparse convolutional networks.