Testability Properties of Divergent Trees

The testability of a class of regular circuits calleddivergent trees is investigated under a functional fault model. Divergent trees include such practical circuits as decoders anddemultiplexers. We prove that uncontrolled divergent trees aretestable with a fixed number of test patterns (C-testable) if andonly if the module function is surjective. Testable controlled treesare also surjective but require sensitizing vectors for errorpropagation. We derive the conditions for testing controlleddivergent trees with a test set whose size is proportional to thenumber of levels p found in the tree (L-testability). By viewing a tree as overlapping arrays of various types, we also deriveconditions for a controlled divergent tree to be C-testable. Typicaldecoders/demultiplexers are shown to only partially satisfy L- andC-testability conditions but a design modification that ensuresL-testability is demonstrated.