This paper describes the development of progressively more powerful and abstract hardware simulators. A small computer hardware design and description language picoella is then introduced, followed by its formal semantics. Using a number of small examples, we will then show the how this formal semantics may be used within a proof system as a sophisticated simulation tool. Examples include some full adders, a general N bit adder, and two parity checkers. Keyword Codes: I.2.3; B.7.2; F.3 Keywords: Deduction and Theorem Proving; Integrated Circuits, Design Aids; Logics and Meaning of Programs 1 Introduction This introduction describes the development of various kinds of hardware simulators. Following this, a small hdl called picoella, is introduced in section 2. Its formal semantics, and a brief account of this semantics' embedding in a proof system are described in section 3. Section 4 illustrates the use of the semantics in the capacity of a symbolic simulator, as described in the rema...