Digital encoders are electro-mechanical sensors that measure linear or angular position using special binary patterns. The properties of these patterns influence the traits of the resulting encoders, such as their maximum speed, resolution, tolerance to error, or cost to manufacture. We describe a novel set of patterns that can be used in encoders that are simple and compact, but require some initial movement to register their position. Previous designs for such encoders, called absolute incremental encoders, tend to incorporate separate patterns for the functions of tracking incremental movement and determining the absolute position. The encoders in this work, however, use a single pattern that performs both functions, which maximizes information density and yields better resolution. Compared to existing absolute encoders, these absolute incremental encoders are much simpler with fewer pattern tracks and read heads, potentially allowing for lower-cost assembly of high resolution encoders. Furthermore, as the manufacturing requirements are less stringent, we expect such encoders may be suitable for use in D.I.Y. %27maker%27 projects, such as those undertaken recently by our lab.