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 brief, two novel DA-based implementation schemes are proposed for adaptive finite-impulse response filters. Different from conventional DA techniques, our proposed schemes use coefficients as addresses to access a series of lookup tables (LUTs) storing sums of delayed and scaled input samples. Two smart LUT updating methods are developed, and least-mean-square adaptation is performed to update the weights and minimize the mean square error between the estimated and desired output. Results show that our two high-performance designs achieve high speed, low computation complexities, and low area cost.