The ring structure proposed in [6] has five stages because L T / L f is 1.1. Because the ratio of our design for nonoverlapped execution is 2.3, we need eight or more substages. Therefore, we put four stages(eight substages in total) in the ring. IV. CONCLUSIO~UThe self-timed divider structure proposed in this brief requires less chip area and maintains higher hardware utilization than the previous implementations employing array or ring structures. The structure is more efficient in terms of execution time and chip area due to the adoption of a novel self-timed ring structure and a carrypropagation-free additionhubtraction scheme. A layout was designed using MOSIS 1.2 pm CMOS design rules. The design occupies 5.7 mm2 of silicon area and takes 135 ns for a worst case division operation. A zero-overhead self-timed 160ns 54-b CMOS divider," IEEE J. vol. 26, pp. J. Robertson, "A new class of digital division methods," IRE Trans. A new carry-free division algorithm and its application to a single-chip 1024-b RSA processor," IEEE J.Abstract-FIRE is a novel Fault-Independent algorithm for comhinationall REdundaucy identification. The algorithm is based on a simple concept that a fault which requires a conflict as a necessary condition for its detection is undetectable and hence redundant. FIRE does not use the backtracking-based exhaustive search performed by fault-oriented automatic test generation algorithms, and identifies redundant faults without any search. Our results on benchmark and real circuits indicate that we find a large number of redundancies (about 80% of the combinational redundancies in benchmark circuits), much faster than a test-generationbased approach for redundancy identification. However, FIRE is not guaranteed to identify all redundancies in a circuit.Index Terms-Redundancy identification, automatic test generation, logic synthesis.

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In this paper, we first present an algorithm (FILL) to efficiently identify a large subset of illegal states in synchronous sequential circuits, without assuming a global reset mechanism. A second algorithm, FUNI, finds sequentially untestable faults whose detection requires some of the illegal states computed by FILL. Although based on binary decision diagrams (BDDs), FILL is able to process large circuits by using a new functional partitioning procedure. The incremental building of the set of illegal states guarantees that FILL will always obtain at least a partial solution. FUNI is a direct method that identifies untestable faults without using the exhaustive search involved in automatic test generation (ATG). Experimental results show that FUNI finds a large number of untestable faults up to several orders of magnitude faster than an ATG algorithm that targeted the faults identified by FUNI. Also, many untestable faults identified by FUNI were aborted by the test generator.

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