Abstract: Quantum-dot Cellular Automata (QCA) which was proposed as a transistor-less paradigm is looked at as a compeer to the Field Effect Transistor (FET). Mapping of the existing technology to this new quantum dot paradigm necessitates bringing in the QCA structures that can perform all the logic operations that are executed in the current technology. Many QCA structures that perform all logic operations were proposed. QCA is exploited in this paper to implement Boolean expressions using Shannon's theorem, a method which breaks down a large function into smaller function. The layouts are simulated using QCA Designer Tool.