Visual odometry is a popular area of computer vision that has seen a paradigm shift towards direct methods, where whole image alignment is used to determine camera poses. Current methods not robust to lighting changes in the scene and rely on standard feature-based methods for multi-camera systems. Binary descriptors are an option for alleviating both problems, but current methods do not scale well to larger and more robust descriptors. We present a method for performing direct tracking with binary descriptors of any size by approximating the gradient and descent direction with Hamming weights. We also present alternative methods that approximate the entire descriptor by its Hamming weights. Our results show improved accuracy compared to tracking on intensity alone, and our primary method improves significantly upon similar methods.