Design of self-checking circuits for unsystematic codes

A new algorithm is proposed for the design of self-checking circuits for a new subset of codes. A classification of the synthesis methods based on the property of groupability of Boolean functions is described. In this paper is presented a new method for the systematic design of self-checking code error detecting circuits with 100% fault coverage for single stuck-at-faults. The new algorithm for the systematic design of an optimal on-line error detecting circuit is based on functional properties and on the functional decomposition. The property of groupability of Boolean functions is used for a selective algorithm based on Boolean differential operations. We can test these properties for any function K by Boolean differential equations in a maximal operation complexity of O(n²) where n is the number of code variables. For example, it is proved, that 50% of all Boolean functions are multiple antivalent groupable. In the presentation the development of code error detecting self-checking circuits is described for unsystematic codes, i.e. the design of self-checking two-rail checkers for antivalent groupable codes K and the design of self-checking multi-rail checkers for conjunctive groupable codes K with a self-checking comparator. The objective of the new approach is to minimize the gate area of the chip. The result of the approach is, that the gate area is approximately 40% lower than by using the method of on-line error detection by duplication and comparison of the self-checking checker