Low-precision weights and activations in deep neural networks (DNNs) outperform their full-precision counterparts in terms of hardware efficiency. When implemented with low-precision operations, specifically in the extreme case where network parameters are binarized (i.e. BNNs), the two most frequently mentioned benefits of quantization are reduced memory consumption and a faster inference process. In this paper, we introduce a third advantage of very low-precision neural networks: improved fault-tolerance attribute. We investigate the impact of memory faults on state-of-the-art binary neural networks (BNNs) through comprehensive analysis. Despite the inclusion of floating-point parameters in BNN architectures to improve accuracy, our findings reveal that BNNs are highly sensitive to deviations in these parameters caused by memory faults. In light of this crucial finding, we propose a technique to improve BNN dependability by restricting the range of float parameters through a novel deliberately uniform quantization. The introduced quantization technique results in a reduction in the proportion of floating-point parameters utilized in the BNN, without incurring any additional computational overheads during the inference stage. The extensive experimental fault simulation on the proposed BNN architecture (i.e. ZOBNN) reveal a remarkable 5X enhancement in robustness compared to conventional floating-point DNN. Notably, this improvement is achieved without incurring any computational overhead. Crucially, this enhancement comes without computational overhead. \ToolName~excels in critical edge applications characterized by limited computational resources, prioritizing both dependability and real-time performance.