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High resolution diagnosis plays a critical role in silicon debug and yield improvement. Application-dependent diagnosis is also a key component in online testing and adaptive computing. In this paper, a new technique for high resolution localization of faults in the interconnects and logic blocks of an arbitrary design implemented on a field-programmable gate array (FPGA) is presented. This work is complementary to application-independent detection methods for FPGAs. This technique can uniquely identify any single bridging, open, or stuck-at fault in the interconnect as well as any single functional fault, a fault resulting a change in the truth table of a function, in the logic blocks. The number of test configurations for interconnect diagnosis is logarithmic to the size of the mapped design, whereas logic diagnosis is performed in only one test configuration with less than 5% overhead of built-in self diagnosis. These techniques have been further extended for multiple fault diagnosis.