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switching circuit theory wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 see also 2 references 3 further reading toggle the table of contents switching circuit theory 3 languages فارسی bahasa indonesia português edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia mathematical study of switched networks switching circuit theory is the mathematical study of the properties of networks of idealized switches such networks may be strictly combinational logic in which their output state is only a function of the present state of their inputs or may also contain sequential elements where the present state depends on the present state and past states in that sense sequential circuits are said to include memory of past states an important class of sequential circuits are state machines switching circuit theory is applicable to the design of telephone systems computers and similar systems switching circuit theory provided the mathematical foundations and tools for digital system design in almost all areas of modern technology 1 in an 1886 letter charles sanders peirce described how logical operations could be carried out by electrical switching circuits 2 during 1880 1881 he showed that nor gates alone or alternatively nand gates alone can be used to reproduce the functions of all the other logic gates but this work remained unpublished until 1933 3 the first published proof was by henry m sheffer in 1913 so the nand logical operation is sometimes called sheffer stroke the logical nor is sometimes called peirce s arrow 4 consequently these gates are sometimes called universal logic gates 5 in 1898 martin boda described a switching theory for signalling block systems 6 7 eventually vacuum tubes replaced relays for logic operations lee de forest s modification in 1907 of the fleming valve can be used as a logic gate ludwig wittgenstein introduced a version of the 16 row truth table as proposition 5 101 of tractatus logico philosophicus 1921 walther bothe inventor of the coincidence circuit got part of the 1954 nobel prize in physics for the first modern electronic and gate in 1924 konrad zuse designed and built electromechanical logic gates for his computer z1 from 1935 to 1938 the theory was independently established through the works of nec engineer akira nakashima in japan 8 claude shannon in the united states 9 and victor shestakov in the soviet union 10 the three published a series of papers showing that the two valued boolean algebra can describe the operation of switching circuits 7 11 12 13 1 however shannon s work has largely overshadowed the other two and despite some scholars arguing the similarities of nakashima s work to shannon s their approaches and theoretical frameworks were markedly different 14 also implausible is that shestakov s influenced the other two due to the language barriers and the relative obscurity of his work abroad 14 furthermore shannon and shestakov defended their theses the same year in 1938 15 and shestakov did not publish until 1941 15 ideal switches are considered as having only two exclusive states for example open or closed in some analysis the state of a switch can be considered to have no influence on the output of the system and is designated as a don t care state in complex networks it is necessary to also account for the finite switching time of physical switches where two or more different paths in a network may affect the output these delays may result in a logic hazard or race condition where the output state changes due to the different propagation times through the network see also edit circuit switching message switching packet switching fast packet switching network switching subsystem 5ess switching system number one electronic switching system boolean circuit boolean differential calculus c element circuit complexity circuit minimization karnaugh map logic design logic gate logic in computer science nonblocking minimal spanning switch programmable logic controller computer software mimics relay circuits for industrial applications quine mccluskey algorithm relay an early kind of logic device switching lemma unate function references edit 1 2 stanković radomir s in german astola jaakko tapio in finnish eds 2008 reprints from the early days of information sciences ticsp series on the contributions of akira nakashima to switching theory pdf tampere international center for signal processing ticsp series vol 40 tampere university of technology tampere finland isbn 978 952 15 1980 2 issn 1456 2774 archived from the original pdf on 2021 03 08 cite book cs1 maint location missing publisher link 3 207 1 pages 10 00 min peirce charles sanders 1993 1886 letter peirce to a marquand writings of charles s peirce vol 5 pp 421 423 see also burks arthur walter 1978 review charles s peirce the new elements of mathematics bulletin of the american mathematical society review 84 5 913 918 917 doi 10 1090 s0002 9904 1978 14533 9 peirce charles sanders 1933 winter of 1880 1881 a boolian algebra with one constant collected papers manuscript vol 4 paragraphs 12 20 reprinted in writings of charles s peirce vol 4 reprint ed 1989 pp 218 221 isbn 9780253372017 ark 13960 t11p5r61f see also roberts don d 2009 the existential graphs of charles s peirce p 131 kleine büning hans lettmann theodor 1999 propositional logic deduction and algorithms cambridge university press p 2 isbn 978 0 521 63017 7 bird john 2007 engineering mathematics newnes p 532 isbn 978 0 7506 8555 9 boda martin 1898 die schaltungstheorie der blockwerke the switching theory of block systems organ für die fortschritte des eisenbahnwesens in technischer beziehung fachblatt des vereins deutscher eisenbahn verwaltungen in german neue folge xxxv 1 7 wiesbaden germany c w kreidel s verlag 1 7 29 34 49 53 71 75 91 95 111 115 133 138 nb this series of seven articles was republished in a 91 pages book in 1899 with a foreword by georg barkhausen de 1 2 klir george jiří may 1972 reference notations to chapter 1 introduction to the methodology of switching circuits 1 ed binghamton new york usa litton educational publishing inc d van nostrand company p 19 isbn 0 442 24463 0 lccn 72 181095 c4463 000 3 p 19 although the possibility of establishing a switching theory was recognized by m boda a as early as in the 19th century the first important works on this subject were published by a nakashima b and c e shannon c shortly before world war ii xvi 573 1 pages nakashima akira may 1936 theory of relay circuit composition nippon electrical communication engineering 3 197 226 nb translation of an article which originally appeared in japanese in the journal of the institute of telegraph and telephone engineers of japan jittej september 1935 150 731 752 shannon claude elwood 1938 a symbolic analysis of relay and switching circuits transactions of the american institute of electrical engineers 57 12 american institute of electrical engineers aiee 713 723 doi 10 1109 t aiee 1938 5057767 hdl 1721 1 11173 s2cid 51638483 nb based on shannon s master thesis of the same title at massachusetts institute of technology in 1937 shestakov шестаков victor ivanovich виктор иванович 1938 некоторые математические методы кон струирования и упрощения двухполюсных электрических схем класса а some mathematical methods for the construction and simplification of two terminal electrical networks of class a phd thesis in russian lomonosov state university yamada 山田 akihiko 彰彦 2004 history of research on switching theory in japan ieej transactions on fundamentals and materials 124 8 institute of electrical engineers of japan 720 726 bibcode 2004ijtfm 124 720y doi 10 1541 ieejfms 124 720 archived from the original on 2022 07 10 retrieved 2022 10 26 switching theory relay circuit network theory theory of logical mathematics ipsj computer museum information processing society of japan 2012 archived from the original on 2021 03 22 retrieved 2021 03 28 stanković radomir s in german astola jaakko tapio in finnish karpovsky mark g 2007 some historical remarks on switching theory pdf niš serbia tampere finland boston massachusetts usa citeseerx 10 1 1 66 1248 s2cid 10029339 archived pdf from the original on 2022 10 25 retrieved 2022 10 25 cite book cite uses deprecated parameter citeseerx help cs1 maint location missing publisher link 8 pages 1 2 kawanishi toma 2019 prehistory of switching theory in japan akira nakashima and his relay circuit theory historia scientiarum second series 29 1 136 162 doi 10 34336 historiascientiarum 29 1_136 1 2 moisil gr c 1969 the algebraic theory of switching circuits pergamon press pp 12 17 isbn 9781483160764 further reading edit keister william ritchie alistair e washburn seth h 1951 the design of switching circuits the bell telephone laboratories series 1 ed d van nostrand company inc p 147 archived from the original on 2020 05 09 retrieved 2020 05 09 2 xx 556 2 pages caldwell samuel hawks 1958 12 01 february 1958 written at watertown massachusetts usa switching circuits and logical design 5th printing september 1963 1st ed new york usa john wiley sons inc lccn 58 7896 xviii 686 pages isbn 0 47112969 0 perkowski marek a grygiel stanislaw 1995 11 20 6 historical overview of the research on decomposition a survey of literature on function decomposition pdf version iv functional decomposition group department of electrical engineering portland university portland oregon usa citeseerx 10 1 1 64 1129 archived pdf from the original on 2021 03 28 retrieved 2021 03 28 cite book cite uses deprecated parameter citeseerx help 188 pages stanković radomir s in german sasao tsutomu astola jaakko tapio in finnish august 2001 publications in the first twenty years of switching theory and logic design pdf tampere international center for signal processing ticsp series tampere university of technology ttkk monistamo finland issn 1456 2774 s2cid 62319288 14 archived from the original pdf on 2017 08 09 retrieved 2021 03 28 4 60 pages stanković radomir s in german astola jaakko tapio in finnish 2011 written at niš serbia tampere finland from boolean logic to switching circuits and automata towards modern information technology studies in computational intelligence vol 335 1 ed berlin heidelberg germany springer verlag doi 10 1007 978 3 642 11682 7 isbn 978 3 642 11681 0 issn 1860 949x lccn 2011921126 retrieved 2022 10 25 xviii 212 pages v t e digital electronics components transistor resistor inductor capacitor printed electronics printed circuit board electronic circuit flip flop memory cell combinational logic sequential logic logic gate boolean circuit integrated circuit ic hybrid integrated circuit hic mixed signal integrated circuit three dimensional integrated circuit 3d ic emitter coupled logic ecl erasable programmable logic device epld macrocell array programmable logic array pla programmable logic device pld programmable array logic pal generic array logic gal complex programmable logic device cpld field programmable gate array fpga field programmable object array fpoa application specific integrated circuit asic tensor processing unit tpu theory digital signal boolean algebra logic synthesis logic in computer science computer architecture digital signal digital signal processing circuit minimization switching circuit theory gate equivalent design logic synthesis place and route placement routing transaction level modeling register transfer level hardware description language high level synthesis formal equivalence checking synchronous logic asynchronous logic finite state machine hierarchical state machine applications computer hardware hardware acceleration digital audio radio digital photography digital telephone digital video cinematography television electronic literature design issues metastability runt pulse retrieved from https en wikipedia org w index php title switching_circuit_theory oldid 1359255852 categories circuit complexity digital circuits digital electronics hidden categories articles with short description short description matches wikidata use dmy dates from october 2022 use list defined references from september 2022 cs1 errors deprecated parameters cs1 maint location missing publisher cs1 interwiki linked names cs1 long volume value cs1 german language sources de cs1 uses russian language script ru cs1 russian language sources ru cs1 location test this page was last edited on 14 june 2026 at 04 16 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia legal safety contacts code of conduct developers statistics cookie statement mobile view search search toggle the table of contents switching circuit theory 3 languages add topic