Fuzzy binary logic modeling of a digital devices

The problem of fuzzy binary logic modeling for discrete devices (DD) is investigated. In contrast to the classical problem of logic simulation, it is assumed that inputs are fuzzy signals. In the real DD for each input signals "0" and "1" there is a certain voltage range. If an input signal is out of the range, the correct signal identification is not guaranteed. The fuzziness of input signals means that their observed values can be either within of the defined range, or out of it. It is clear that the corresponding output signal of the DD will be also fuzzy. It is known that the modeling of every logical DD is the calculation of the value of the certain logical expression. This expression is a mathematical model of the DD. Also, the corresponding expression can be always represented in terms of three logical operations, namely, AND, OR, and NOT. In the article, a method of reducing the investigated problem to the problem of fuzzy modeling systems in the space of real numbers is proposed. This method is based on the presentation of logical operations through operations of addition, subtraction, and multiplication of real numbers in the range [0, 1]. So, it is proposed to convert the input signal range into sub-intervals of the interval [0, 1] forming the specific calibration scale. The problem of fuzzy modeling systems in the space of real numbers has been well studied and the arsenal of tools for its solution is developed. Therefore, we can use this arsenal. However, the implementation of this approach is very time-consuming. The matter is that an exemplary fuzzy modeling system requires the sequential execution of three phases (blocks). Two of them (the INFERENCE block and DEFUZZIFICATION block) are connected with a lot of computing. The proposed fuzzy binary logic simulation procedure consists of two phases. The first phase is the conversion of voltage ranges representing the input signals into sub-intervals of the interval [0, 1] of the calibration scale. Then, the calculation of the arithmetic expression that is originated by the mathematical model of the considered DD is performed. In the second phase, the transformation of fuzzy value of the expression in the exact value 0 or 1 (defuzzification) is executed. In comparison with the above mention typical fuzzy system modeling, the suggested modeling procedure is significantly less complicated. It is because of the block INFERENCE is absent in our procedure. Moreover, converting fuzzy output value in the exact value is performed by using extremely simple rules, in contrast to the labor-intensive transformations for the typical fuzzy modeling. The results of testing for the combinational circuit are shown. The effectiveness of the procedure is demonstrated by a number of correct results.

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