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A novel artificial neural network (SYNTHESIS-ANN) is presented, which has been designed for computationally intensive problems and applied to the optimization of antennas and microwave devices. The antenna example presented is optimized with respect to voltage standing-wave ratio, bandwidth, and frequency of operation. A simple microstrip transmission line problem is used to further describe the ANN effectiveness, in which microstrip line width is optimized with respect to line impedance. The ANNs exploit a unique number representation of input and output data in conjunction with a more standard neural network architecture. An ANN consisting of a heteroassociative memory provided a very efficient method of computing necessary geometrical values for the antenna when used in conjunction with a new randomization process. The number representation used provides significant insight into this new method of fault-tolerant computing. Further work is needed to evaluate the potential of this new paradigm.