Neural image codecs achieve higher compression ratios than traditional hand-crafted methods such as PNG or JPEG-XL, but often incur substantial computational overhead, limiting their deployment on energy-constrained devices such as smartphones, cameras, and drones. We propose Grayscale Image Compression with Differentiable Logic Circuits (GIC-DLC), a hardware-aware codec where we train lookup tables to combine the flexibility of neural networks with the efficiency of Boolean operations. Experiments on grayscale benchmark datasets show that GIC-DLC outperforms traditional codecs in compression efficiency while allowing substantial reductions in energy consumption and latency. These results demonstrate that learned compression can be hardware-friendly, offering a promising direction for low-power image compression on edge devices.