This paper introduces the concept of system semantics, an extension of the denotational theory of programming languages, to the description of arbitrary systems. For a given formal description, different meaning functions describe different properties of interest concerning the system, e.g., structure, behaviour, performance. The meaning functions can be made sufficiently simple to serve equally well as rules for formal reasoning and as an actual system description language (SDL) implementation. These principles are first demonstrated in the area of digital systems, which represent the class of systems with unidirectional information flow, and subsequently in the area of analog circuits, where information flow is bidirectional. It is shown how semantic functions can be used to derive properties, ranging from general theorems of circuit theory, expressed as conversion rules in the language, to special conditions for particular circuits, expressed as equations in the meta- language.