The problems of typing and structuring data were investigated. An algorithm definition reflecting an important property of alternacy has been introduced. In the classical theory of algorithms, provisions are distinguished that provide two principles of a modern digital computer: program control of program execution and placement of the executed program in memory along with other data. Possible structures of algorithms, algorithmically insoluble problems, complexity of algorithms, abstract models of computers are considered. We have studied the logical foundations of a computer, methods for representing and transforming data in various number systems, and performing basic arithmetic and logical operations.