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Quantization of the parameters of a Perceptron is a central problem in hardware implementation of neural networks using a numerical technology. A neural model with each weight limited to a small integer range will require little surface of silicon. Moreover, according to Occam's razor principle, better generalization abilities can be expected from a simpler computational model. The price to pay for these benefits lies in the difficulty to train these kind of networks. This paper proposes essentially two new ideas for constructive training algorithms, and demonstrates their efficiency for the generation of feedforward networks composed of Boolean threshold gates with discrete weights. A proof of the convergence of these algorithms is given. Some numerical experiments have been carried out and the results are presented in terms of the size of the generated networks and of their generalization abilities.