Self-checking combinational circuits with unidirectionally independent outputs

In this paper we propose a structure dependent method for the systematic design of a self-checking circuit which is well adapted to the fault model of single gate faults and which can be used in test mode. According to the fault model considered, maximal groups of independent and unidirectionally independent outputs of an arbitrarily given combinational circuit are determined. A parity bit is added to every group of independent outputs. A few additional outputs are added to every group of unidirectionally independent outputs. In the error free case, these groups of unidirectional independent outputs together with their corresponding additional outputs are elements of a unidirectional error detecting code; for example, a Berger code or an r-out-of-s code. It is demonstrated how the pairs of (unidirectionally) independent outputs of a given circuit can be determined. A simple heuristic solution for this problem based on a modified circuit graph is also given. The maximal classes of (unidirectionally) independent outputs can be computed as cliques of a dependency graph where the nodes of the graph are the outputs of the circuit. The applicability of the proposed method is demonstrated for the MCNC benchmarks circuits.