A method for synthesis of computing and controlling contact circuits

The author generalizes Gavrilov's and Shannon's results concerning cascaded networks and proves the formula (A) from which he deduces a simple and rapid method for synthesis of bridge-type and multioutput contact circuits. This new cascade method offers the designer a concise step-by-step algorithm resulting in considerable time saving and circuitry reduction. The basic idea of the method is to expand switching functions according to the formula (Б), to unite their coefficients as in Table 1, and to interpret such a compressed expansion table graphically as in Fig. 6 or 7 for Table 1 (the author uses the European switching algebra). Six illustrative examples are given: combinatorial binary adder, combinatorial binary subtracter, combinatorial decimal inverter, circuit for binary-number comparison, code translator for subscriber's pulses, and symmetrical lattice. Although the method developed here is powerful, it is no design panacea. Other possibilities of circuitcy reduction should not be ignored. The method is especially suited to symmetrical cirfuits for which it yields a better solution than Shannon's earlier method [3]. A method ror recognizing the circuit symmetry based on the theory of groups is presented in my paper [18]. A short preliminary communication on the cascade method was published in my paper [9].The symbolic method of D. Zeheb and W. P. Caywood [21] is in essence a particular case of the cascade method as applied to two-terminal circuits. The cascade method is also compared with the universal-network method [8] and F. Svoboda's method [13]. The Appendix shows how the basic idea of the cascade method could be applied to the functional synthesis of electronic, rectifier, and transformer logical circuits. The notion of divergent logical circuits is introduced. These are analogous to bridge-type contact circuits. The cascade method gives an algorithm for designing divergent and multioutput logical circuits. The formula (Г) for transformer logical circuits is deduced.