Article

Article title THE SYNTESIS OF BINARY FLIP-FLOP CIRCUITS IN LINEAR ALGEBRA
Authors N.V. Butyrlagin, N.N. Prokopenko, N.I. Chernov, V.Y. Yugay
Section SECTION II. COMPUTER ENGINEERING AND COMPUTER SCIENCE
Month, Year 02, 2015 @en
Index UDC 681.5:681.3(075.8)
DOI
Abstract Some other types of algebras can be used instead of Boolean algebra as a mathematical apparatus for logic synthesis of digital structures. The linear Algebra – algebraic structure А→(А; +, ∙, θ; P), in which Р→(Р; +, ∙, 0,1) – field, θ – zero vector and А→(А; +, ∙, θ; P) − vector (linear) space overa field P is proposed as an alternative mathematical apparatus. Set of vectors of the corresponding dimension for the linear space is a basic set of this structure. In this case the set of Boolean vectors is a subset of the space vectors for a linear space. The simplification of the digital structures circuitry, improving their technical and operational characteristics are advantages of linear algebra. The possibility of using the linear algebra apparatus for synthesis of the binary trigger structures is considered in this paper. The linear-algebraic interpretation of binary logic functions by linear operations is shown. The truncation difference is chosen as the basic operation for forming basis vectors. The simplicity of circuit implementation, ie minimum hardware is the selection factor. The synthesis method for the logic elements of the flip-flop structures, based on linear algebra, is described. The linear elements of memory structures and the simplest type of the flip-flops, which are based on the results of logic synthesis solutions, are proposed. The implementations of the flip-flop circuits, based on bipolar transistors, are proposed. The simulation of a binary memory cells are given, the simulation circuits, timing diagrams of the memory cells, as well as assessing the impact of various destabilizing factors on the quality of the memory cell operation are presented.

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Keywords Linear logic synthesis; hybrid basis; differential representation of logic functions; non-classical synthesis; Boolean linear space.
References 1. Melikyan V., Balabanyan A., Durgaryan A. Noise Effect Estimation and Reduction in High-Speed Voltage Controlled Oscillators, Proceedings of IEEE East-West Design & Test Symposium (EWDTS’2013). Rostov-on-Don, September 27–30, 2013, pp. 19-22.
2. Chernov N.I. Osnovy logicheskogo sinteza tsifrovykh struktur nad polem veshchestvennykh chisel [Fundamentals of logic synthesis of digital structures over the field of real numbers]. Taganrog: TRTU, 2000, 146 p.
3. Chernov N.I. Bulevo lineynoe prostranstvo kak algebraicheskaya struktura dlya logicheskogo sinteza tsifrovykh ustroystv [Boolean linear space as an algebraic structure for logic synthesis of digital devices], Izvestiya TRTU [Izvestiya TSURe], 2003, No. 1 (30), pp. 73-76.
4. Chernov N.I. Strukturnyy sintez tsifrovykh ustroystv v bulevykh lineynykh prostranstvakh [Structural synthesis of digital devices in Boolean linear spaces], Izvestiya TRTU [Izvestiya TSURe], 2003, No. 2 (31), pp. 215-220.
5. Chernov N.I. Lineynyy sintez tsifrovykh struktur ASOiU: Uchebnoe posobie [Linear synthesis of the digital structures of the information processing system: a tutorial]. Taganrog: Izd-vo TRTU, 2004, 147 p.
6. Chernov N.I. Effektivnost' primeneniya apparata lineynykh prostranstv v logicheskom sinteze tsfrovykh struktur» [Efficacy of linear spaces in the logical synthesis of the digital structures"], Trudy Mezhdunarodnykh nauchno-tekhnicheskikh konferentsiy «Intellektual'nye sistemy (IEEE AIS’05)» i «Intellektual'nye SAPR (CAD-2005») [Proceedings of International
scientific-technical conference "Intelligent systems (IEEE AIS'05) and" Intelligent CAD "(CAD-2005"), Vol. 1, pp. 420-424.
7. Chernov N.I. Logicheskoe proektirovanie tsifrovykh struktur na upravlyaemykh generatorakh toka [Logical design of digital structures on managed generators], Izvestiya TRTU [Izvestiya TSURe], 2005, No. 11 (55), pp. 77-83.
8. Chernov N.I. Logicheskiy sintez tsifrovykh struktur v lineynykh algebrakh [Logical synthesis of the digital structures in linear algebras], Materialy V Mezhdunarodnogo nauchno-prakticheskogo seminara «Problemy sovremennoy analogovoy mikroshemotekhniki» [Materials of V International scientific-practical seminar "problems of modern analog micro circuitry"]. Shakhty, 2006, pp. 27-36.
9. Chernov N.I., Yugay V.Ya. Neklassicheskiy sintez tsifrovykh struktur sredstvami analogovoy skhemotekhniki [Non-classical synthesis of the digital structures by means of analog circuitry], Materialy IX Mezhdunarodnogo nauchno-prakticheskogo seminara «Problemy sovremennoy analogovoy mikroshemotekhniki». (Shakhty, 1–3 noyabrya 2012 goda) [Materials of IX International scientific-practical seminar "problems of modern analog micro circuitry". (Shakhty, 1-3 November 2012). ha h y: FGBOU VPO «YuRGUE », 2012.
10. Chernov N.I., Yugay V.Ya. Neklassicheskiy sintez tsifrovykh struktur sredstvami analogovoy skhemotekhniki [Non-classical synthesis of the digital structures by means of analog circuitry], Problemy sovremennoy analogovoy skhemotekhniki: Cb. materialov IX Mezhdunarodnogo
nauchno-prakticheskogo seminara [Problems of modern analog circuit design: proceedings of the IX International scientific-practical seminar]. Shakhty: Izd-vo FGBOU VPO «YuRGUE », 2012, pp. 138-143.
11. Chernov N.I. Effektivnost' primeneniya apparata lineynykh prostranstv v logicheskom sinteze tsifrovykh struktur [Efficacy of linear spaces in the logical synthesis of the digital structures], Trudy Mezhdunarodnykh nauchno-tekhnicheskikh konferentsiy «Intellektual'nye sistemy (IEEE AIS’05)» i «Intellektual'nye SAPR (CAD-2005») [Proceedings of International scientific-technical conference "Intelligent systems (IEEE AIS'05) and" Intelligent CAD "(CAD-2005")], Vol. 1, pp. 420-424.
12. Chernov N.I. Lineynyy podkhod kak perspektiva sovershenstvovaniya tsifrovoy elementnoy bazy. Voprosy spetsial'noy mikroelektroniki. Seriya "Obshchie voprosy radioelektroniki» [The linear approach as the prospect of improving digital element base. The special issues of microelectronics. Series "General electronics"], Nauchno-tekhn. sbornik [Scientific and technical collection], Issue 2. Taganrog: TNIIS, 2011, pp. 122-132.
13. Chernov N.I., Yugay V.Ya. Osobennosti sinteza posledovatel'nostnykh tsifrovykh struktur v lineynoy algebre [Features of synthesis of sequential digital structure in linear algebra], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2011, No. 2 (115), pp. 51-57.
14. Prokopenko N.N., Chernov N.I., Yugay V.Ya. Bazovaya kontseptsiya lineynogo sinteza mnogoznachnykh tsifrovykh struktur v lineynykh prostranstvakh [The basic concept of linear synthesis of multivalued digital structures in linear spaces], Trudy kongressa po intellektual'nym sistemam i informatsionnym tekhnologiyam IS&IT’13 [Proceedings of the
Congress on intelligent systems and information technology IS&IT’13]. Moscow: Fizmatlit, 2013, pp. 284-289.
15. Prokopenko N.N., Chernov N.I., Yugay V.Ya. Lineynyy logicheskiy sintez dvuznachnykh tsifrovykh struktur v lineynykh prostranstvakh [Linear logic synthesis two-digit numeric structures in linear spaces], Trudy kongressa po intellektual'nym sistemam i informatsionnym tekhnologiyam IS&IT’13 [Proceedings of the Congress on intelligent systems and information chnology I &IT’13]. Moscow: Fizmatlit, 2013, pp. 278-283.
16. Prokopenko N.N., Chernov N.I., Yugay V.Ya. Bazovaya kontseptsiya lineynogo sinteza mnogoznachnykh tsifrovykh struktur v lineynykh prostranstvakh [The basic concept of linear synthesis of multivalued digital structures in linear spaces], Kongress «IS&IT’13». «Intellektual'nye sistemy’13», «Intellektual'nye SAPR-2013»: trudy konferentsiy [Congress
IS&IT'13". "Intelligent systems'13", "Intelligent CAD systems-2013": conference proceedings]. Moscow: Fizmatlit, 2013, Vol. 1, pp. 284.
17. Prokopenko N.N., Chernov N.I., Yugay V.Ya. Lineynyy logicheskiy sintez dvuznachnykh tsifrovykh struktur v lineynykh prostranstvakh [Linear logic synthesis two-digit numeric structures in linear spaces], Kongress «IS&IT’13». «Intellektual'nye sistemy’13», «Intellektual'nye SAPR-2013»: trudy konferentsiy [Congress “IS&IT'13". "Intelligent systems'13", "Intelligent
CAD systems-2013": conference proceedings]. M: Fizmatlit, 2013, Vol. 1, pp. 278-283.
18. Chernov N.I., Yugai V.Ya., Prokopenko N.N., Butyrlagin N.V. Вasic Concept of Linear Synthesis of Multi-Valued Digital Structures in Linear Spaces, Proceedings of IEEE East-Wesr Design & Test Simposium (E DT ’2 13), Rostov-on-Don, September 27-30, 2013. Kharkov National University of Radioelectronics, pp. 146-149.
19. Karpenko A.S. Mnogoznachnye logiki. Logika i komp'yuter [Many-valued logic. Logic and computer]. Moscow: Nauka, 1997, Issue 4, 223 p.
20. Sayt po troichnoy logike [The website on ternary logic]. Available at: http://ternarycomp.cs.msu.su/index.html.

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