In this work, a fast digital device is defined, which is customized to implement an artificial neuron. Its high computational speed is obtained by mapping data from floating point to integer residue representation, and by computing neuron functions through residue arithmetic operations, with the use of table look-up techniques. Specifically, the logic design of a residue neuron is described and complexity figures of area occupancy and time consumption of the proposed device are derived. The approach was applied to the logic design of a residue neuron with 12 inputs and with a Residue Number System defined in such a way as to attain an accuracy better than or equal to the accuracy of a 20-bit floating point system. The proposed design (NEUROM) exploits the RNS carry independence property to speed up computations, in addition it is very suitable for using look-up tables. The response time of our device is about 8xTACC, where TACC is the ROM access time. With a value of TACC close to the 10 ns allowed by the current ROM technology, the proposed neuron responds within 80 ns, NEUROM is therefore the neuron device proposed in the literature which allows for maximum throughput. Moreover, when a pipeline mode of operation is adopted, the pipeline delay can assume a value as low as about 14 ns. In the case study considered, the total amount of ROM is about 5.55 Mbits. Thus, using current technology, it is possible to integrate several residue neurons into a single VLSI chip, thereby enhancing chip throughput. The paper also discusses how this amount of memory could be reduced, at the expense of the response time.