Summary: We consider a generalization of functions, which are called “binary self-similar functions” by Bl. Kh. Sendov [Fundam. Prikl. Mat. 5, No. 2, 589–595 (1999; Zbl 0973.28005)]. In this paper, we analyze the connections of the object of study with well known classes of fractal functions, with the geometry of numerical series, with distributions of random variables with independent random digits of the two-symbol \(Q_2\)-representation, with theory of fractals. Structural, variational, integral, differential and fractal properties are studied for the functions of this class.