Non-exhaustive Parity Testing

In this paper, some new approaches are presented to deal with the dilemma we are facing in using parity testing: (1) proposing a method of turning a parity untestable circuit into parity testable (2) presenting a scheme of replacing the exhaustive testing with nonexhaustive way. The parity testing may resume its spirits by using some new technologies including the way presented here. I. Parity and Its Properties The parity of F, denoted by P(F), is defined as P(F) = K(F) mod 2, where K(F) is the number of all minterms of the function of F. Theorem: Let N be a circuit realizing the function of F(x1, x2, ..., xn ), and Fα(x1, x2, ..., xn ) be the faulty function with a stuck-at-fault α on xi (i = 1, 2, ..., n), then the number of minterms of the faulty function must be even, i.e. P(Fα) = 0. A circuit is called Parity Testable if any single stuckat-fault occurring on signal lines will cause an erroneous parity (i.e. a parity complementary to that of fault-free circuit), and is called I/O (External) Parity Testable if a fault occurring only on I/O pins of the circuit can produce an erroneous parity. Now, we may conclude directly from the above theorem that a circuit with an odd parity must be I/O (external) parity testable. In order to facilitate the derivation of the parities for a combinational circuit, the following new way can be used based on Boolean Difference.