Most Analog Devices digital potentiometers (with the notable exception of the AD8400/AD8402/AD8403) contain power-on reset (POR) circuitry, which presets the wiper to terminal resistance to the middle value of the terminal to terminal resistance. For example, if the end to end resistance (RAB) = 10 kΩ, at power-up, RWB = RWA = 5 kΩ, where RWB is the resistance between Terminal W and Terminal B and RWA is the resistance between Terminal W and Terminal A. For the digital potentiometers that do not have this feature, the wiper to terminal resistance can be anything at power-up. See the relevant product data sheet for more details.