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Distributed arithmetic (DA) is performed to design bit-level architectures for vector-vector multiplication with a direct application for the implementation of convolution, which is necessary for digital filters. In this work, a DA based FIR adaptive filter implementation scheme is proposed. Different from existing DA schemes, our proposed scheme uses coefficients as addresses to access a series of look-up tables (LUTs) storing sums of delayed and scaled input samples. With least mean square (LMS) adaptation, offset-binary coding (OBC) based LUT updating method is presented as well. Results show that our high performance design achieves high-speed, low computation complexity, and low area cost.