As humans, we inherently perceive images based on their predominant features, and ignore noise embedded within lower bit planes. On the contrary, Deep Neural Networks are known to confidently misclassify images corrupted with meticulously crafted perturbations that are nearly imperceptible to the human eye. In this work, we attempt to address this problem by training networks to form coarse impressions based on the information in higher bit planes, and use the lower bit planes only to refine their prediction. We demonstrate that, by imposing consistency on the representations learned across differently quantized images, the adversarial robustness of networks improves significantly when compared to a normally trained model. Present state-of-the-art defenses against adversarial attacks require the networks to be explicitly trained using adversarial samples that are computationally expensive to generate. While such methods that use adversarial training continue to achieve the best results, this work paves the way towards achieving robustness without having to explicitly train on adversarial samples. The proposed approach is therefore faster, and also closer to the natural learning process in humans.