This paper presents the design of distributed embedded systems using the synchronous multiclock model of the Signal language. It proposes a methodology that ensures a correct-by-construction functional implementation of these systems from high-level models. It shows the capability of the synchronous approach to apply formal techniques and tools that guarantee the reliability of the designed systems. Such a capability is necessary and highly worthy when dealing with safety-critical systems. The proposed methodology is demonstrated through a case study consisting of a simple avionic application, which aims to pragmatically help the reader to understand the manipulated formal concepts, and to apply them easily in order to solve system correctness issues encountered in practice. The application functionality is first modeled as well as its distribution on a generic hardware architecture. This relies on the endochrony and endo-isochrony properties of Signal specifications, defined previously. The considered architectures include asynchronous communication mechanisms, which are also modeled in Signal and proved to achieve message exchanges correctly. Furthermore, the synchronizability of the different parts in the resulting system is addressed after its deployment on a specific execution platform with multirate clocks. After all these steps, a distributed code can be automatically generated.