Abstract—A circuit may produce unknown output values during simulation of a test set, e.g., due to an unknown initial state or due to the existence of tristate elements. Unknown output values in the output response of a circuit make it impossible to determine a single unique signature for the fault-free circuit when built-in self-test is used for testing the circuit. We consider the problem of synthesizing a logic block that replaces unknown output values in the output response of a circuit with a known constant. The logic block is constructed from building blocks called comparison units. The synthesis procedure ensures that the built-in self-test scheme will be able to detect all the faults detectable by the test set applied to the circuit while allowing a single unique signature to be computed. Two variations of the synthesis procedure are considered, a two-dimensional version suitable for synchronous sequential circuits without scan and for scan circuits with multiple scan chains and a one-dimensional version suitable for scan circuits with a single scan chain.