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A new hardware implementation of the triangular neighborhood function (TF) for ultra-low power, self-organizing maps (SOM) is presented. Simulations carried out in the software model of this network show that even for low signal resolutions (3-6 bits) performance of the network is not affected. Resolution of the signal at the output of this block has a dominant influence on the circuit complexity as well as the energy consumption. The proposed mechanism is very fast. For a neighborhood range of 15 a delay in the circuit equals 20 ns that allows for data rates of 20- 40 MHz, even for large maps with several hundreds neurons.