Abstract: A method and apparatus for an electronic artificial neural network, which serves as an associative memory that has a complete set of N-dimensional Hadamard vectors as stored states, suitable for large N that are powers of 2. The neural net has nonlinear synapses, each of which processes signals from two neurons. These synapses can be implemented by simple passive circuits comprised of eight resistors and four diodes. The connections in the neural net are specified through a subset of a group that is defined over the integers from 1 to N. The subset is chosen such that the connections can be implemented in VLSI or wafer scale integration. An extension of the Hadamard memory causes the memory to provide new Hadamard vectors when these are needed for the purpose of Hebb learning.