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This paper deals with the family of CMAC neural networks. The most important properties of this family are the extremely fast learning capability and a special architecture that makes effective digital hardware implementation possible. The paper gives an overview of the classical binary CMAC, shows the limitations of its modelling capability, gives a critical survey of its different extensions and suggests two further modifications. ; The aim of these modifications is to improve the modelling capability while maintaining the possibility of an effective realization. The basic element of the first suggested hardware structure is a new matrix-vector multiplier which is based on a canonical signed digit (CSD) number representation and a distributed arithmetic. ; In the other version, a hierarchical network structure and a special sequential training method are proposed which can constitute a trade-off between the approximation error and generalization. The proposed versions (among them a dynamic extension of the originally static CMAC) are suitable for embedded applications where the low cost and relatively high speed operation are the most important requirements.