A binary number can indeed be viewed as an orthogonal basis, where each digit position corresponds to a new dimension. This perspective aligns with the principles of the Discrete Fourier Transform (DFT), where each binary digit functions as a discrete component. The mathematical framework supports this interpretation, particularly within the context of the field ##\mathbb{Z}_2## and its n-dimensional unit cube representation. Understanding this relationship enhances comprehension of both binary representation and Fourier analysis in information theory.
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Yes. Since ##\mathbb{Z}_2## is a field everything is fine in ##\mathbb{Z}_2^n##, the ##n-##dimensional unit cube.entropy1 said:Could you view a discrete number, for instance a binary number, as a sort of orthogonal basis, where each digit position represents a new dimension? I see similarities between a binary number and for instance Fourier Transform, with each digit being a discrete function.