Universal logic circuits and their modular realizations

Abstract

In order to achieve the great economic advantage of utilizing integrated circuits in computer circuitry, it is desirable to design a circuit which can realize any logic function of a fixed number of variables by simply varying its input terminal connections. Such a circuit is called a universal logic circuit (ULC). When the number of variables becomes large, a ULC may be too complex to be built in a single package economically. Hence, it is preferred to use ULC's of a small number of variables as the modules to build a ULC of a large number of variables. Such modules are called universal logic modules (ULM's). In this paper, we shall first present a three-variable ULC, which has a fan-in for each logic gate not exceeding four, and consists of only 7 I/O pins. Then, we shall extend the ULC's to four or more variables. There are 12 I/O pins in a ULC of four variables, and several models with different fan-in limitations will be given. The logic gates in the ULC's may be all NAND or all NOR gates. Then, a simple technique for designing a ULC of any large number of variables using the ULC's of a small number of variables, say three variables, as the ULM's will be established. It will be seen that the ULC obtained by this technique will require a small number of ULM's. Moreover, the fault-detection tests for ULM's and a diagnostic procedure for locating all the faulty ULM's in the modular realization of a ULC realizing a given logic function will be presented. Finally, a method for improving the reliability of a ULC using an error-correcting code will be demonstrated.