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Simplification of the diagram of a threshold element


A.S. Nikolaev – Ph.D.(Eng.), Associate Professor, Department «Computer systems and networks», Kaluga branch of the Bauman MSTU
M.Yu. Aliev – Head of Department, JSC «Typhoon» (Kaluga)

On an output of a threshold element unit level is set if the quantity of units on its inputs exceeds some threshold. A special case of a threshold element is the majority element. The majority element has odd quantity of inputs. The signal on its output accepts value of unit if more, than at a half of its inputs there is unit. Threshold and majority elements found broad application in technique during creation of different devices. However complexity of such elements sharply increases with increase in quantity of their inputs. In too time, elements with a large number of inputs allow to solve more complex problems. The existing methods of minimization of logic functions aren't adjusted for use for the functions having a large number of arguments. Therefore often complexity of elements with a large number of inputs is a basic reason of a failure from creation of the equipment using such elements.
In article the method of minimization of function of a threshold element based on partition of a set of his arguments on groups is offered. At the same time the problem of minimization of function of threshold function with a large number of arguments is replaced with the task of minimization of function of a threshold element with twice smaller quantity of inputs. As a result the task of minimization becomes technically solvable. The results of minimization given in examples can be used as ready decisions. At the same time they show the considerable abbreviation of number of the logical actions executed when calculating function in comparison with other methods of minimization. Recommendations about partition of arguments on the groups allowing to receive the best minimization option from all possible are made. The choice of option of partition of arguments on groups is also confirmed by examples.

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