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This paper studies the stability of a quantized feedback control system. In recent years, there have been a number of papers characterizing the minimum information rate required to assure closed loop stability. An inherent constraint on these quantized control systems is that the number of quantization levels must be an integer. In our opinion, insufficient attention has been paid to this constraint. This paper takes these integral constraints into account to establish a lower bound on the number of quantization levels required for closed loop stability. We then introduce a novel dynamic bit assignment policy that achieves this bound.