In this paper, we introduce a memory-efficient CNN (convolutional neural network), which enables resource-constrained low-end embedded and IoT devices to perform on-device vision tasks, such as image classification and object detection, using extremely low memory, i.e., only 63 KB on ImageNet classification. Based on the bottleneck block of MobileNet, we propose three design principles that significantly curtail the peak memory usage of a CNN so that it can fit the limited KB memory of the low-end device. First, 'input segmentation' divides an input image into a set of patches, including the central patch overlapped with the others, reducing the size (and memory requirement) of a large input image. Second, 'patch tunneling' builds independent tunnel-like paths consisting of multiple bottleneck blocks per patch, penetrating through the entire model from an input patch to the last layer of the network, maintaining lightweight memory usage throughout the whole network. Lastly, 'bottleneck reordering' rearranges the execution order of convolution operations inside the bottleneck block such that the memory usage remains constant regardless of the size of the convolution output channels. The experiment result shows that the proposed network classifies ImageNet with extremely low memory (i.e., 63 KB) while achieving competitive top-1 accuracy (i.e., 61.58\%). To the best of our knowledge, the memory usage of the proposed network is far smaller than state-of-the-art memory-efficient networks, i.e., up to 89x and 3.1x smaller than MobileNet (i.e., 5.6 MB) and MCUNet (i.e., 196 KB), respectively.