Abstract
The continued fraction expansion and the binary expansion provide two of the most widely-used methods of description of a real number by means of a sequence of integers. By relating the two codings, we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, and discuss the \exceptional parameters for these families. By means of this dictionary, one can recover results about the real slice of the Mandelbrot set, and the set of univoque numbers.
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