Abstract: The paper reviews existing methods of mathematical description and representation of algorithms for data conversion operations (arithmetic operations, calculation of elementary functions (EF) and others).  The article shows that their main realizations in the computer at the various levels of the organization of computational process are software, firmware and circuit realizations. As a possible way of mathematical representation the authors consider table representation, representation based on the systems of Boolean functions and Turing machine based representation. The article presents a brief analysis of the known forms of representation of systems of Boolean functions (SBF), taking into account the means of implementation and evaluation of mathematical and technical complexity depending on the type of description. The representation of the data transformation algorithms as SBF maximizes parallelization of data conversion. It is shown that the computational complexity of the operation is determined by the power of the input and output sets and number of bits in input and resulting data. The representation of the algorithms based on systems of Boolean functions in the form of the PDNF is highly redundant which is shown on the example of some arithmetic operations. The authors make a conclusion about the need of minimizing the complexity based on the minimum and shortest form of SBF. As a way of implementing SBF in the FPLD the authors considered use of the universal logic modules (ULM), in technical terms that a lookup table (LUT). The article present methods of constructing SBF based on the ULM of four variables and methods of SBF SBF decomposition for its implementation in ULM schemes. Methods and research methodology include mixed methods analysis methods, methods of the theory of discrete mathematics, apparatus for analysis and synthesis of Boolean functions in particular, the theory of algorithms, methods of computational experiment. The article reviews the complexity of the mathematical representation of the data conversion operations and their implementation in the computer (arithmetic computations, elementary functions and some others). The authors suggest algorithms for implementation of the SBF in form of ULM scheme of four variables, study the algorithms for constructing such schemes based on the Shannon and Reed expansions. Based on the analysis of the input and output variables of data conversion operations the  SBF synthesis for the formation of problem-oriented and specialized computer commands is carried out.