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Integrating Fast Karnough Map and Modular Neural Networks for Simplification and Realization of Complex Boolean Functions

Authors: Hazem M. El-Bakry


In this paper a new fast simplification method is presented. Such method realizes Karnough map with large number of variables. In order to accelerate the operation of the proposed method, a new approach for fast detection of group of ones is presented. Such approach implemented in the frequency domain. The search operation relies on performing cross correlation in the frequency domain rather than time one. It is proved mathematically and practically that the number of computation steps required for the presented method is less than that needed by conventional cross correlation. Simulation results using MATLAB confirm the theoretical computations. Furthermore, a powerful solution for realization of complex functions is given. The simplified functions are implemented by using a new desigen for neural networks. Neural networks are used because they are fault tolerance and as a result they can recognize signals even with noise or distortion. This is very useful for logic functions used in data and computer communications. Moreover, the implemented functions are realized with minimum amount of components. This is done by using modular neural nets (MNNs) that divide the input space into several homogenous regions. Such approach is applied to implement XOR function, 16 logic functions on one bit level, and 2-bit digital multiplier. Compared to previous non- modular designs, a clear reduction in the order of computations and hardware requirements is achieved.

Keywords: Boolean functions, simplification, Karnough map, implementation of logic functions, modular neural networks.

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