Dense depth prediction deep neural networks (DNN) have achieved impressive results for both monocular and binocular data but they are limited by high computational complexity, restricting their use on low-end devices. For better on-device efficiency and hardware utilization, weights and activations of the DNN should be converted to low-bit precision. However, this precision is not sufficient for representing high dynamic range depth. In this paper, we aim to overcome this limitation and restore high-precision depth from low-bit precision predictions. To achieve this, we propose to represent high dynamic range depth as two low dynamic range components of a Hilbert curve, and to train the full precision DNN to directly predict the latter. For on-device deployment, we use standard quantization methods and add a post-processing step that reconstructs depth from the Hilbert curve components predicted in low-bit precision. Extensive experiments demonstrate that our method increases bit precision of predicted depth by up to three bits with little computational overhead. We also observe a positive side effect of quantization error reduction by up to five times. Our method enables effective and accurate depth prediction with DNN weights and activations quantized to eight bit precision.