Increasing demands for massive data transmission pose significant challenges to communication systems. Compared with traditional communication systems that focus on the accurate reconstruction of bit sequences, semantic communications (SemComs), which aim to deliver information connotation, are regarded as a key technology for sixth-generation (6G) mobile networks. Most current SemComs utilize an end-to-end (E2E) trained neural network (NN) for semantic extraction and interpretation, which lacks interpretability for further optimization. Moreover, NN-based SemComs assume that the application and physical layers of the protocol stack can be jointly trained, which is incompatible with current digital communication systems. To overcome those drawbacks, we propose a SemCom system that employs explicit semantic bases (Sebs) as the basic units to represent semantic connotations. First, a mathematical model of Sebs is proposed to build an explicit knowledge base (KB). Then, the Seb-based SemCom architecture is proposed, including both a communication mode and a KB update mode to enable the evolution of communication systems. Sem-codec and channel codec modules are designed specifically, with the assistance of an explicit KB for the efficient and robust transmission of semantics. Moreover, unequal error protection (UEP) is strategically implemented, considering communication intent and the importance of Sebs, thereby ensuring the reliability of critical semantics. In addition, a Seb-based SemCom protocol stack that is compatible with the fifth-generation (5G) protocol stack is proposed. To assess the effectiveness and compatibility of the proposed Seb-based SemComs, a case study focusing on an image-transmission task is conducted. The simulations show that our Seb-based SemComs outperform state-of-the-art works in learned perceptual image patch similarity (LPIPS) by over 20% under varying communication intents and exhibit robustness under fluctuating channel conditions, highlighting the advantages of the interpretability and flexibility afforded by explicit Sebs.