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Test resources can be embedded on the chip to reduce required external tester channels. In order to obtain the maximal reduction of tester channels, a single-output encoder based on the check matrix of the (n, n-1, m, 3) convolutional code is presented. When the five proposed theorems are satisfied, the encoder can avoid two and any odd erroneous bit cancellations, handle one unknown bit (X-bit), and diagnose one erroneous bit. Two types of encoders are proposed to implement the check matrix of the convolutional code. A large number of X-bits can be tolerated by choosing a proper memory size and weight of the check matrix, which can also be obtained by an optimized input assignment algorithm. In order to get the full diagnostic capability, the proposed encoder can be reconfigured into a simple linear-code-based encoder by adding some additional gates. Experimental results show that the proposed encoder has an acceptable level of X-bits tolerance and a low aliasing probability.