A Symbolic Analysis of Relay and Switching Circuits

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| author = Claude E. Shannon

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| orig_lang_code = en

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| country = United States

| language = English

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| subject = Switching circuit theory

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| pub_date = 1938

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A Symbolic Analysis of Relay and Switching Circuits is the title of a master's thesis written by computer science pioneer Claude E. Shannon while attending the Massachusetts Institute of Technology (MIT) in 1937,{{Cite book |last1=Agarwal |first1=Ravi P |url=https://books.google.com/books?id=bENTBQAAQBAJ&dq=claude+shannon+master%27s+thesis+1936&pg=PA425 |title=Creators of Mathematical and Computational Sciences |last2=Sen |first2=Syamal K |date=2014 |publisher=Springer International Publishing |isbn=978-3-319-10869-8 |location=Cham |pages=425 |language=en |doi=10.1007/978-3-319-10870-4}}{{Cite book |last=Fox |first=Charles |url=https://books.google.com/books?id=aHO1EAAAQBAJ&dq=claude+shannon+worked+on+his+master%27s+thesis+in+1936&pg=PA114 |title=Computer Architecture: From the Stone Age to the Quantum Age |date=2024 |publisher=No Starch Press |isbn=978-1-7185-0286-4 |location=San Francisco |pages=114 |language=en}} and then published in 1938. In his thesis, Shannon, a dual degree graduate of the University of Michigan, proved that Boolean algebra{{Cite book

| last = Caldwell

| first = Samuel H.

| author-link = Samuel H. Caldwell

| title = Switching Circuits and Logical Design, Sixth Printing

| publisher = John Wiley & Sons

| location = New York

| year = 1965

| orig-year = 1958

| page = 34

| isbn = 978-0471129691

| quote = [Shannon] constructed a calculus based on a set of postulates which described basic switching ideas; e.g., an open circuit in series with an open circuit is an open circuit. Then he showed that his calculus was equivalent to certain elementary parts of the calculus of propositions, which in turn was derived from the algebra of logic developed by George Boole.

}} could be used to simplify the arrangement of the relays that were the building blocks of the electromechanical automatic telephone exchanges of the day. He went on to prove that it should also be possible to use arrangements of relays to solve Boolean algebra problems. His thesis laid the foundations for all digital computing and digital circuits.{{Cite book |last=Wheen |first=Andrew |url=https://books.google.com/books?id=B6shu_hAiGkC |title=Dot-Dash to Dot.Com: How Modern Telecommunications Evolved from the Telegraph to the Internet |date=2011 |publisher=Springer New York |isbn=978-1-4419-6759-6 |location=New York, NY |pages=77 |language=en |doi=10.1007/978-1-4419-6760-2}}{{Cite book |last=Wright |first=Alex |author-link=Alex Wright |url=https://books.google.com/books?id=Fd2gEAAAQBAJ |title=Informatica: Mastering Information through the Ages |date=2023 |publisher=Cornell University Press |isbn=978-1-5017-6867-5 |pages=188 |language=en |jstor=10.7591/j.ctv2rtgnvk }}

The utilization of the binary properties of electrical switches to perform logic functions is the basic concept that underlies all electronic digital computer designs. Shannon's thesis became the foundation of practical digital circuit design when it became widely known among the electrical engineering community during and after World War II. At the time, the methods employed to design logic circuits (for example, contemporary Konrad Zuse's Z1) were ad hoc in nature and lacked the theoretical discipline that Shannon's paper supplied to later projects.

Shannon's work also differered significantly in its approach and theoretical framework compared to the work of Akira Nakashima. Whereas Shannon's approach and framework was abstract and based on mathematics, Nakashima tried to extend the existent circuit theory of the time to deal with relay circuits, and was reluctant to accept the mathematical and abstract model, favoring a grounded approach.{{Cite journal |last=Kawanishi |first=Toma |date=2019 |title=Prehistory of Switching Theory in Japan: Akira Nakashima and His Relay-circuit Theory |url=https://www.jstage.jst.go.jp/article/historiascientiarum/29/1/29_136/_article |journal=Historia Scientiarum |series=Second Series |volume=29 |issue=1 |pages=136–162 |doi=10.34336/historiascientiarum.29.1_136}} Shannon's ideas broke new ground, with his abstract and modern approach dominating modern-day electrical engineering.

The paper is commonly regarded as the most important master's thesis ever due to its insights and influence.{{Cite book |last=Norman |first=Jeremy M. |url=https://books.google.com/books?id=emmitTbOoFgC&dq=a+mathematical+theory+of+communication+the+most+important+paper&pg=PA749 |title=From Gutenberg to the Internet: A Sourcebook on the History of Information Technology |publisher=Historyofscience.com |year=2005 |isbn=978-0-930405-87-8 |location=Novato, Calif |pages=749 |language=en |oclc=ocm57124414}}{{Cite book |last1=Aleksander |first1=Igor |url=https://books.google.com/books?id=j_S6CgAAQBAJ&dq=Aristotle%27s+Laptop:+The+Discovery+of+our+Informational+Mind+most+important+ms+thesis+ever&pg=PA22 |title=Aristotle's Laptop: The Discovery of our Informational Mind |last2=Morton |first2=Helen |date=2012 |publisher=World Scientific Publishing |isbn=978-981-4343-49-7 |series=Series on Machine Consciousness |volume=1 |pages=22 |language=en |doi=10.1142/8113}}{{Cite book |last1=Matthews |first1=Suzanne J. |url=https://books.google.com/books?id=ZX85EAAAQBAJ&dq=claude+shannon+masters+thesis+most+important+thesis&pg=PA234 |title=Dive Into Systems: A Gentle Introduction to Computer Systems |last2=Newhall |first2=Tia |last3=Webb |first3=Kevin C. |publisher=No Starch Press |year=2022 |isbn=978-1-7185-0136-2 |location=San Francisco |pages=234 |language=en}}{{Cite tweet |number=1737360314440786070 |user=pmddomingos |title=The most important master's thesis of all time. |first=Pedro |last=Domingos |author-link=Pedro Domingos |date=2023-12-20 |access-date=2024-11-05}} Pioneering computer scientist Herman Goldstine described Shannon's thesis as "surely{{nbsp}}... one of the most important master's theses ever written{{nbsp}}... It helped to change digital circuit design from an art to a science."{{refn|{{cite book|page=119-20|title=The Computer: From Pascal to von Neumann|last=Goldstine|first=Herman A.|year=1972}} }} In 1985, psychologist Howard Gardner called his thesis "possibly the most important, and also the most famous, master's thesis of the century".{{Cite web |last=Smith |first=Nancy Duvergne |date=2011-08-15 |title=Claude Shannon: Digital Pioneer's Work Still Reverberates |url=https://alum.mit.edu/slice/claude-shannon-digital-pioneers-work-still-reverberates |access-date=2024-01-11 |website=alum.mit.edu |language=en}} The paper won the 1939 Alfred Noble Prize.

A version of the paper was published in the 1938 issue of the Transactions of the American Institute of Electrical Engineers.{{cite journal

|last = Shannon

|first = C. E.

|author-link = Claude Elwood Shannon

|title = A Symbolic Analysis of Relay and Switching Circuits

|journal = Trans. AIEE

|year = 1938

|volume = 57 |issue=12

|pages = 713–723

|doi= 10.1109/T-AIEE.1938.5057767

|hdl = 1721.1/11173

|s2cid = 51638483