Digital Simulation with Multiple Logic Values

Multiple-valued logics have long been used, often in intuitive fashion, for simulating transients, errors, unknown states, variable-strength signals, etc., in binary digital circuits. This paper presents a rigorous algebraic method for analyzing such logics, and for systematically constructing new ones. Starting with a basis such as 2-valued Boolean algebra, new algebras suitable for a broad range of practical simulation tasks are obtained systematically via a small set of expansion operations. This approach is applied in detail to the construction of families of simulation algebras for gate-level logic circuits; switch-level simulation is also considered. It is concluded that current simulation programs frequently lack essential logic values, and occasionally have superfluous ones. Some major discrepancies in the number of distinct logic values claimed by commercial simulators are also explained.