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A direct adaptive control framework for linear uncertain systems with input quantizers is developed. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability; that is, Lyapunov stability of the closed-loop system states and attraction with respect to the plant states. Specifically, the input quantizers are logarithmic and characterized by sector-bound conditions with the conic sector adjusted at each time instant by the adaptive controller in conjunction with the system response. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach.