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The author addresses the problem of designing totally self-checking checkers for checking m two-rail signal pairs, when the checker receives a subset of all possible input codewords, under normal operation. There are cases when a two-rail checker tree, which will be tested by the inputs received under normal operation, cannot be found. However, it is shown that two-rail checker network structures other than trees will also be totally self-checking (TSC) and code-disjoint. A method for designing TSC two-rail checkers for a given set of input codewords is presented.