Karnaugh Maps of Logical Systems and Applications in Digital Circuit Design
| Autor: | Cailu Wang, Yuegang Tao |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Digital electronics
State-transition matrix 0209 industrial biotechnology Sequential logic business.industry Computer science Applied Mathematics 02 engineering and technology 020901 industrial engineering & automation Signal Processing Graph (abstract data type) State (computer science) Arithmetic Karnaugh map business State transition table Hardware_LOGICDESIGN Electronic circuit |
| Zdroj: | Circuits, Systems, and Signal Processing. 39:2245-2271 |
| ISSN: | 1531-5878 0278-081X |
| DOI: | 10.1007/s00034-019-01214-x |
| Popis: | This paper extends the concept of Karnaugh map from a logical function to a logical system, thereby allowing both the state transition graph and state transition matrix of a logical system, as well as a digital circuit, to be constructed directly. It is found that the Karnaugh map of a logical system is actually a two-dimensional state transition table or, equivalently, a table-like state transition graph and is also a grid-type state transition matrix. For constructing the state transition graph and state transition matrix of a logical system, the computational complexities of the methods based on the proposed Karnaugh map are exponentially lower than those of the existing methods. The Karnaugh maps of logical systems are then used in the analysis and design of clocked sequential circuits and in the simplification of multioutput gate circuits. Some illustrative examples and simulations are presented to demonstrate the results and their applications. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink