Abstract: Apparatus and Methods for performing arithmetic operations in a predetermined base and arithmetic logic units are provided. In one example, the apparatus comprises a non-linear medium. The apparatus further comprises one or more photon sources for outputting photons in a first frequency band and a second frequency band towards the non-linear medium, the first frequency band being representative of a first numeric value and the second frequency band being representative of a second numeric value. The apparatus further comprises an input to receive a signal indicative of at least one numeric value. The apparatus further comprises logic to select at least one of the first frequency band and second frequency band in dependence on the signal.