Binary-neural-network based keyword spotting (KWS) for resource-constrained devices has gained much attention in recent years. Although several works proved their success, a fully binary KWS system is yet to come, considering high-precision speech feature maps are still required for satisfying accuracy. Such precision mismatch results in non-binary activation layers, thus leading to extra computational costs. In this paper, we present an extremely compact KWS system using a binary neural network and error-diffusion binarized speech features. The system eliminates all high-precision multiplications and requires only hardware-friendly bit-wise operations and additions for inference. Experiments on the Google speech commands show that our binary KWS system yields 98.54% accuracy on a 1-keyword task and 95.05% on a 2-keyword task, outperforming 8-bit KWS systems of bigger size. The result proves the feasibility of a fully binary KWS system and can be inspiring for hardware implementations.