With the recent physical demonstration of memristive-based devices, low-power two terminal devices with memory and learning functions have advanced electronics and computing. In memristive devices, typically slow moving ions are coupled with fast moving electrons. Ionic motion affords memory, with electronic current as the output signal. Here, we present fully ionic memory devices in which protons (H+) provide both memory and output signal. We describe the development of 1D and 2D grid-based memory elements. These devices function by storing and passing protons between adjacent palladium bits, in a mechanism similar to electron transfer in a CCD. This transfer allows for the serial measurement of parallel analog inputs. Digital input or output can easily be accomplished by assigning logic values to threshold values of proton concentration. Energy consumption is dependent on device volume: the current 10ï¿½m x 30 ï¿½m device consumes 35 ï¿½J per switching operation, but a 40nm x 40nm bit is expected to consume less than 50fJ.