# Ring counter

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Type of counter

A **ring counter** is a type of [counter](/source/Counter_(digital)) composed of [flip-flops](/source/Flip-flop_(electronics)) connected into a [shift register](/source/Shift_register), with the output of the last flip-flop fed to the input of the first, making a "circular" or "ring" structure.

There are two types of ring counters:

- A **straight ring counter**, also known as a **[one-hot](/source/One-hot) counter**, connects the output of the last shift register to the first shift register input and circulates a single one (or zero) bit around the ring.

- A **Johnson counter**, also called **twisted ring counter**, **switch-tail ring counter**[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*], **walking ring counter**[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*], or **[Möbius](/source/M%C3%B6bius_band) counter**[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*], connects the last shift register's complemented output to the input of the first register and circulates a stream of ones followed by zeros around the ring.

## Four-bit ring-counter sequences

Straight ring counter Johnson counter State Q0 Q1 Q2 Q3 State Q0 Q1 Q2 Q3 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 2 0 0 1 0 2 1 1 0 0 3 0 0 0 1 3 1 1 1 0 0 1 0 0 0 4 1 1 1 1 1 0 1 0 0 5 0 1 1 1 2 0 0 1 0 6 0 0 1 1 3 0 0 0 1 7 0 0 0 1 0 1 0 0 0 0 0 0 0 0

## Properties

Ring counters are often used in larger [finite-state machines](/source/Finite-state_machines). A binary counter requires [adder](/source/Adder_(electronics)) circuits which have propagation delays that increase as the number of bits increases, whereas the propagation delays within a ring counter are constant regardless of the number of bits.

The straight and twisted forms have different properties, and relative advantages and disadvantages.

A disadvantage of ring counters is that they are lower density codes than [binary encodings](/source/Binary_encoding) of state numbers. A binary counter has 2*N* states, where *N* is the number of bits in the code, whereas a straight ring counter has only *N* states and a Johnson counter has only 2*N* states. This may be an important consideration in hardware implementations where registers are more expensive than combinational logic.

Johnson counters are sometimes favored because they offer twice as many states from the same number of bits, and because they are able to self-initialize from the all-zeros state. The Johnson counter generates a [Gray code](/source/Gray_code) in which adjacent states differ by only one bit (i.e., have a [Hamming distance](/source/Hamming_distance) of 1), which can be useful if the bit pattern will be asynchronously sampled.[1]

When a fully decoded or [one-hot](/source/One-hot) representation of the counter state is needed, as in some sequence controllers, the straight ring counter is usually preferred. The one-hot property means that the set of codes are separated by a [minimum Hamming distance](/source/Minimum_Hamming_distance) of 2,[2] so any single-bit error is detectable.

Sometimes bidirectional shift registers are used (using multiplexors to take the input for each flip-flop from its left or right neighbor), so that bidirectional or up–down ring counters can be made.[3]

## Logic diagrams

The straight ring counter has the logical structure shown here:

Instead of the reset line setting up the initial [one-hot](/source/One-hot) pattern, the straight ring is sometimes made self-initializing by the use of a distributed feedback gate across all of the outputs except that last, so that a 1 is presented at the input when there is no 1 in any stage but the last.[4]

A Johnson counter, named for [Robert Royce Johnson](/source/Robert_Royce_Johnson), is a ring with an inversion; here is a 4-bit Johnson counter:

Note the small bubble indicating inversion of the Q signal from the last shift register before feeding back to the first D input, making this a Johnson counter.

## History

Before the days of digital computing, digital counters were used to measure rates of random events such as radioactive decays to alpha and beta particle. Fast "pre-scaling" counters reduced the rate of random events to more manageable and more regular rates. Five-state ring counters were used along with divide-by-two scalers to make decade (power-of-ten) scalers before 1940, such as those developed by [C. E. Wynn-Williams](/source/C._E._Wynn-Williams).[5]

Early ring counters used only one active element (vacuum tube, valve, or transistor) per stage, relying on global feedback rather than local bistable flip-flops, to suppress states other than the one-hot states, for example in the 1941 patent filing of [Robert E. Mumma](https://en.wikipedia.org/w/index.php?title=Robert_E._Mumma&action=edit&redlink=1) of the [National Cash Register Company](/source/National_Cash_Registor_Company).[6] [Wilcox P. Overbeck](/source/Wilcox_P._Overbeck) invented a version using multiple anodes in a single vacuum tube,[7][8] In recognition of his work, ring counters are sometimes referred to as "Overbeck rings".[9][10]

The [ENIAC](/source/ENIAC) used decimal arithmetic based on 10-state one-hot ring counters. The works of Mumma at [NCR](/source/NCR_Voyix) and Overbeck at [MIT](/source/MIT) were among the prior art works examined by the patent office that invalidated the patents of [J. Presper Eckert](/source/J._Presper_Eckert) and [John Mauchly](/source/John_Mauchly) for the ENIAC technology.[11]

By the 1950s, ring counters with a two-tube or twin-triode flip-flop per stage were appearing.[12]

Robert Royce Johnson developed a number of different shift-register-based counters with the aim of making different numbers of states with the simplest possible feedback logic, and filed for a patent in 1953.[13] The Johnson counter is the simplest of these.

## Applications

Early applications of ring counters were as frequency prescalers (e.g. for [Geiger counter](/source/Geiger_counter) and such instruments),[5] as counters to count pattern occurrences in cryptanalysis (e.g. in the [Heath Robinson codebreaking machine](/source/Heath_Robinson_(codebreaking_machine)) and the [Colossus computer](/source/Colossus_computer)),[14] and as accumulator counter elements for decimal arithmetic in computers and calculators, using either [bi-quinary](/source/Bi-quinary_coded_decimal) (as in the Colossus) or ten-state one-hot (as in the [ENIAC](/source/ENIAC)) representations.

Straight ring counters generate fully decoded one-hot codes to that are often used to enable a specific action in each state of a cyclic control cycle. One-hot codes can also be decoded from a Johnson counter, using one gate for each state.[15][nb 1]

Besides being an efficient alternative way to generate one-hot codes and frequency pre-scalers, a Johnson counter is also a simple way to encode a cycle of an even number of states that can be asynchronously sampled without glitching, since only one bit changes at a time, as in a [Gray code](/source/Gray_code).[16] Early [computer mice](/source/Computer_mice) used up–down (bidirectional) 2-bit Johnson or Gray encodings to indicate motion in each of the two dimensions, though in mice those codes were not usually generated by rings of flip-flops (but instead by electro-mechanical or optical [quadrature encoders](/source/Quadrature_encoder)).[17] A 2-bit Johnson code and a 2-bit Gray code are identical, while for 3 or more bits Gray and Johnson codes are different. In the 5-bit case, the Johnson counter's code is the same as the [Libaw–Craig code](/source/Libaw%E2%80%93Craig_code) [[de](https://de.wikipedia.org/wiki/Libaw-Craig-Code)] for decimal digits, from "a non-counting decimal- coded shaft digitizer".[18][19][20][21][22][23][24][25]

A Johnson counter and a few resistors can produce a glitch-free approximation of a sine wave having an output frequency determined solely by the counter's clock frequency.[26]

Decimal 0 1 2 3 4 5 6 7 8 9 1-bit 1 0 1 0 1 0 1 0 1 0 1 2-bit 2 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 3-bit 3 2 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 4-bit Johnson 4 3 2 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 Libaw–Craig 5 4 3 2 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1-2-1 5 4 3 2 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1-of-10 10 9 8 7 6 5 4 3 2 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

## See also

- [Counter (digital)](/source/Counter_(digital))

- [Ring oscillator](/source/Ring_oscillator)

- [Linear-feedback shift register](/source/Linear-feedback_shift_register)

## Notes

1. **[^](#cite_ref-NB1_16-0)** Johnson counter circuits with single states decoded in this way can be found in the original [IBM](/source/IBM) [MDA](/source/Monochrome_Display_Adapter) and [CGA](/source/Color_Graphics_Adapter) video display adapter designs, in the timing sequencer logic: one or two [74x174](/source/74174) hex D-type flip-flop ICs are wired as a shift register, fed back with inversion to form a Johnson counter, and 2-input [NAND gates](/source/NAND_gate) (in the MDA) or [XOR gates](/source/XOR_gate) (in the CGA) are used to decode states used as signals such as +RAS (Row Address Strobe [to [DRAM](/source/DRAM)]) and S/-L (Shift / NOT Load). Source: IBM Personal Computer Options & Adapters Technical Reference, Monochrome Display and Printer Adapter, logic diagrams; IBM Personal Computer Options & Adapters Technical Reference, Color Graphics Monitor Adapter, logic diagrams.

## References

1. **[^](#cite_ref-Pedroni_2013_1-0)** Pedroni, Volnei A. (2013). [*Finite State Machines in Hardware: Theory and Design*](https://books.google.com/books?id=SSkTDgAAQBAJ&pg=PA50). [MIT Press](/source/MIT_Press). p. 50. [ISBN](/source/ISBN_(identifier)) [978-0-26201966-8](https://en.wikipedia.org/wiki/Special:BookSources/978-0-26201966-8).

1. **[^](#cite_ref-Mengibar_2003_2-0)** Mengibar, Luis; Entrena, Luis; Lorenz, Michael G.; Sánchez-Reillo, Raúl (2003). ["State Encoding for Low-Power FSMs in FPGA"](https://books.google.com/books?id=JEEmfObxnrAC&pg=PA35). *Integrated Circuit and System Design. Power and Timing Modeling, Optimization and Simulation: Proceedings of the 13th International Workshop, PATMOS 2003, Torino, Italy, 10–12 September 2003*. Vol. 13. [Springer Science & Business Media](/source/Springer_Science_%26_Business_Media). p. 35. [ISBN](/source/ISBN_(identifier)) [9783540200741](https://en.wikipedia.org/wiki/Special:BookSources/9783540200741).

1. **[^](#cite_ref-Stan_1997_3-0)** Stan, Mircea R. (1997). ["Synchronous up/down counter with clock period independent of counter size"](http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Stan.pdf) (PDF). *Proceedings 13th IEEE Symposium on Computer Arithmetic*: 274–281.

1. **[^](#cite_ref-Holdsworth_2002_4-0)** Holdsworth, Brian; Woods, Clive (2002). [*Digital Logic Design*](https://books.google.com/books?id=o7enSwSVvgYC&pg=PA192) (4 ed.). [Newnes Books](/source/Newnes_Books) / [Elsevier Science](/source/Elsevier_Science). pp. 191–192. [ISBN](/source/ISBN_(identifier)) [0-7506-4588-2](https://en.wikipedia.org/wiki/Special:BookSources/0-7506-4588-2). Retrieved 2020-04-19.{{[cite book](https://en.wikipedia.org/wiki/Template:Cite_book)}}: CS1 maint: ignored ISBN errors ([link](https://en.wikipedia.org/wiki/Category:CS1_maint:_ignored_ISBN_errors)) (519 pages) [\[1\]](https://web.archive.org/web/20200419213939/http://s2.bitdownload.ir/Ebook/Electronics/Holdsworth%20-%20Digital%20Logic%20Design%204e%20HQ%20(Newnes,%202002).pdf)

1. ^ [***a***](#cite_ref-Lewis_1942_5-0) [***b***](#cite_ref-Lewis_1942_5-1) [Lewis, Wilfrid Bennett](/source/Wilfrid_Bennett_Lewis) (1942). [*Electrical Counting: With Special Reference to Counting Alpha and Beta Particles*](https://books.google.com/books?id=5B5CDAAAQBAJ&pg=PA90). [Cambridge University Press](/source/Cambridge_University_Press). p. 90. [ISBN](/source/ISBN_(identifier)) [9781316611760](https://en.wikipedia.org/wiki/Special:BookSources/9781316611760). {{[cite book](https://en.wikipedia.org/wiki/Template:Cite_book)}}: ISBN / Date incompatibility ([help](https://en.wikipedia.org/wiki/Help:CS1_errors#invalid_isbn_date))

1. **[^](#cite_ref-Mumma_1941_6-0)** ["Electronic accumulation", Robert E. Mumma's US Patent No. 2405096, filed in 1941](https://patents.google.com/patent/US2405096)

1. **[^](#cite_ref-Overbeck_1943_7-0)** ["Electronic switching device", Wilcox P. Overbeck's US Patent No. 2427533, filed in 1943](https://patents.google.com/patent/US2427533)

1. **[^](#cite_ref-Dayton_8-0)** [Dayton Codebreakers: 1942 Research Report, mentioning "A new high speed counter by Mr. Overbeck, January 8, 1942"](http://daytoncodebreakers.org/depth/42_res_rpt/)

1. **[^](#cite_ref-RAMAC_1959_9-0)** [*RAMAC 305 - IBM Customer Engineering Manual of Instruction*](http://www.ed-thelen.org/RAMAC/IBM-227-3534-0-305-RAMAC-r.pdf) (PDF). [IBM](/source/IBM). 1959. […] The Overbeck ring is used to supply timed pulses within computer circuits much as cam operated circuit breakers supply timed pulses on mechanical machines. It consists of a set of triggers with a common input from the *ring drive line* which carries pulses supplied by the process drum. […] Initially the triggers are reset OFF with the exception of the *home* trigger, which is ON. Each negative input pulse will turn OFF the trigger that is ON. The fall of the voltage at pin 10 of the trigger being turned OFF will grid flip the next trigger ON. This continues through a closed ring […]

1. **[^](#cite_ref-US_1960_10-0)** [*Electrical Technology - A Suggested 2-Year Post High School Curriculum*](https://books.google.com/books?id=0zoUAAAAIAAJ&q=%22overbeck+ring%22). Technical Education Program Series. United States, Division of Vocational and Technical Education. 1960. p. 52.

1. **[^](#cite_ref-Randall_2014_11-0)** Randall, Brian (2014). ["The Origins of Digital Computers: Supplementary Bibliography"](https://books.google.com/books?id=AsvSBQAAQBAJ&pg=PA652). In Metropolis, Nicholas (ed.). *History of Computing in the Twentieth Century*. Elsevier. pp. 651–652. [ISBN](/source/ISBN_(identifier)) [9781483296685](https://en.wikipedia.org/wiki/Special:BookSources/9781483296685).

1. **[^](#cite_ref-Higinbotham_1949_12-0)** [William Alfred Higinbotham](/source/William_Alfred_Higinbotham), ["Fast impulse circuits"](https://patents.google.com/patent/US2536808A/en), US Patent No. 2536808, filed in 1949

1. **[^](#cite_ref-Johnson_1953_13-0)** [Robert Royce Johnson](/source/Robert_Royce_Johnson), ["Electronic counter"](https://patents.google.com/patent/US3030581A/en), US Patent No. 3030581, filed in 1953

1. **[^](#cite_ref-Copeland_2010_14-0)** Copeland, B. Jack (2010). *Colossus: The Secrets of Bletchley Park's Code-breaking Computers*. [Oxford University Press](/source/Oxford_University_Press). pp. 123–128. [ISBN](/source/ISBN_(identifier)) [978-0-19957814-6](https://en.wikipedia.org/wiki/Special:BookSources/978-0-19957814-6).

1. **[^](#cite_ref-Langholz_1998_15-0)** Langholz, Gideon; Kandel, Abraham; Mott, Joe L. (1998). [*Foundations of Digital Logic Design*](https://books.google.com/books?id=4sX9fTGRo7QC&pg=PA525). World Scientific. pp. 525–526. [ISBN](/source/ISBN_(identifier)) [978-9-81023110-1](https://en.wikipedia.org/wiki/Special:BookSources/978-9-81023110-1).

1. **[^](#cite_ref-Holten_1982_17-0)** van Holten, Cornelius (August 1982). Written at Delft Technical University, Delft, Netherlands. ["Digital dividers with symmetrical outputs - The author uses Johnson counters with controlled feedback to give symmetrical even and odd-numbered divisions of a clock pulse"](https://worldradiohistory.com/hd2/IDX-UK/Technology/Technology-All-Eras/Archive-Wireless-World-IDX/80s/Wireless-World-1982-08-OCR-Page-0024.pdf) (PDF). *[Wireless World](/source/Wireless_World)*. Vol. 88, no. 1559. Sutton, Surrey, UK: [IPC Business Press Ltd.](/source/IPC_Business_Press_Ltd.) pp. 43–46. [ISSN](/source/ISSN_(identifier)) [0043-6062](https://search.worldcat.org/issn/0043-6062). [Archived](https://web.archive.org/web/20210221205532/https://worldradiohistory.com/hd2/IDX-UK/Technology/Technology-All-Eras/Archive-Wireless-World-IDX/80s/Wireless-World-1982-08-OCR-Page-0024.pdf) (PDF) from the original on 2021-02-21. Retrieved 2021-02-20. [\[2\]](https://web.archive.org/web/20210221205421/https://worldradiohistory.com/hd2/IDX-UK/Technology/Technology-All-Eras/Archive-Wireless-World-IDX/80s/Wireless-World-1982-08-OCR-Page-0025.pdf) [\[3\]](https://web.archive.org/web/20210221205307/https://worldradiohistory.com/hd2/IDX-UK/Technology/Technology-All-Eras/Archive-Wireless-World-IDX/80s/Wireless-World-1982-08-OCR-Page-0026.pdf) (4 pages)

1. **[^](#cite_ref-Lyon_1981_18-0)** [Lyon, Richard F.](/source/Richard_F._Lyon) (August 1981), [*The Optical Mouse, and an Architectural Methodology for Smart Digital Sensors*](http://www.bitsavers.org/pdf/xerox/parc/techReports/VLSI-81-1_The_Optical_Mouse.pdf) (PDF) (Report), Palo Alto Research Center, Palo Alto, California, USA: [Xerox Corporation](/source/Xerox_Corporation), VLSI 81-1, [archived](https://web.archive.org/web/20200523093939/http://www.bitsavers.org/pdf/xerox/parc/techReports/VLSI-81-1_The_Optical_Mouse.pdf) (PDF) from the original on 2020-05-23, retrieved 2020-05-23, The counters needed for X and Y simply count through four states, in either direction (up or down), changing only one bit at a time (i.e., 00, 01, 11, 10). This is a simple case of either a Gray-code counter or a Johnson counter (Moebius counter). (41 pages)

1. **[^](#cite_ref-Libaw-Craig_1953_19-0)** Libaw, William H.; Craig, Leonard J. (October 1953) [September 1953]. ["A Photoelectric Decimal-Coded Shaft Digitizer"](https://www.researchgate.net/publication/224112055). *[Transactions of the I.R.E. Professional Group on Electronic Computers](/source/Transactions_of_the_I.R.E._Professional_Group_on_Electronic_Computers)*. **EC-2** (3): 1–4. [doi](/source/Doi_(identifier)):[10.1109/IREPGELC.1953.5407731](https://doi.org/10.1109%2FIREPGELC.1953.5407731). [eISSN](/source/EISSN_(identifier)) [2168-1759](https://search.worldcat.org/issn/2168-1759). [ISSN](/source/ISSN_(identifier)) [2168-1740](https://search.worldcat.org/issn/2168-1740). Retrieved 2020-05-26. (4 pages)

1. **[^](#cite_ref-Powell_1968_20-0)** Powell, E. Alexander (June 1968). "Codes particularly useful for analogue to digital conversions". [*A short note on useful codes for Fluidic Control Circuits*](https://dspace.lib.cranfield.ac.uk/bitstream/handle/1826/9559/COA_Memo_156_June_1968.pdf) (PDF). Cranfield, UK: [The College of Aeronautics](/source/College_of_Aeronautics%2C_Cranfield), Department of Production Engineering. p. 10. [S2CID](/source/S2CID_(identifier)) [215864694](https://api.semanticscholar.org/CorpusID:215864694). CoA Memo 156. [Archived](https://web.archive.org/web/20201215124905/https://dspace.lib.cranfield.ac.uk/bitstream/handle/1826/9559/COA_Memo_156_June_1968.pdf) (PDF) from the original on 2020-12-15. Retrieved 2020-12-15. (18 pages) (NB. The paper names the [Glixon code](#Glixon) *modified Gray code* and misspells [Richard W. Hamming](/source/Richard_W._Hamming)'s name.)

1. **[^](#cite_ref-Dokter_1973_21-0)** Dokter, Folkert; Steinhauer, Jürgen (1973-06-18). [*Digital Electronics*](https://books.google.com/books?id=hlRdDwAAQBAJ). Philips Technical Library (PTL) / Macmillan Education (Reprint of 1st English ed.). Eindhoven, Netherlands: [The Macmillan Press Ltd.](/source/The_Macmillan_Press_Ltd.) / [N. V. Philips' Gloeilampenfabrieken](/source/N._V._Philips'_Gloeilampenfabrieken). p. 43. [doi](/source/Doi_(identifier)):[10.1007/978-1-349-01417-0](https://doi.org/10.1007%2F978-1-349-01417-0). [ISBN](/source/ISBN_(identifier)) [978-1-349-01419-4](https://en.wikipedia.org/wiki/Special:BookSources/978-1-349-01419-4). [SBN](/source/SBN_(identifier)) [333-13360-9](https://en.wikipedia.org/wiki/Special:BookSources/0-333-13360-9). Retrieved 2020-05-11. (270 pages)

1. **[^](#cite_ref-Dokter_1975_1_22-0)** Dokter, Folkert; Steinhauer, Jürgen (1975) [1969]. *Digitale Elektronik in der Meßtechnik und Datenverarbeitung: Theoretische Grundlagen und Schaltungstechnik*. Philips Fachbücher (in German). Vol. I (improved and extended 5th ed.). Hamburg, Germany: [Deutsche Philips GmbH](/source/Deutsche_Philips_GmbH). pp. 52, 58, 98. [ISBN](/source/ISBN_(identifier)) [3-87145-272-6](https://en.wikipedia.org/wiki/Special:BookSources/3-87145-272-6). (xii+327+3 pages)

1. **[^](#cite_ref-Dokter_1975_2_23-0)** Dokter, Folkert; Steinhauer, Jürgen (1975) [1970]. *Digitale Elektronik in der Meßtechnik und Datenverarbeitung: Anwendung der digitalen Grundschaltungen und Gerätetechnik*. Philips Fachbücher (in German). Vol. II (4th ed.). Hamburg, Germany: [Deutsche Philips GmbH](/source/Deutsche_Philips_GmbH). p. 169. [ISBN](/source/ISBN_(identifier)) [3-87145-273-4](https://en.wikipedia.org/wiki/Special:BookSources/3-87145-273-4). (xi+393+3 pages)

1. **[^](#cite_ref-Steinbuch_1962_24-0)** [Steinbuch, Karl W.](/source/Karl_W._Steinbuch), ed. (1962). Written at Karlsruhe, Germany. *Taschenbuch der Nachrichtenverarbeitung* (in German) (1 ed.). Berlin / Göttingen / New York: [Springer-Verlag OHG](/source/Springer-Verlag_OHG). pp. 71–72, 74. [LCCN](/source/LCCN_(identifier)) [62-14511](https://lccn.loc.gov/62-14511).

1. **[^](#cite_ref-Steinbuch_1967_25-0)** [Steinbuch, Karl W.](/source/Karl_W._Steinbuch); Wagner, Siegfried W., eds. (1967) [1962]. *Taschenbuch der Nachrichtenverarbeitung* (in German) (2 ed.). Berlin, Germany: [Springer-Verlag OHG](/source/Springer-Verlag_OHG). [LCCN](/source/LCCN_(identifier)) [67-21079](https://lccn.loc.gov/67-21079). Title No. 1036.

1. **[^](#cite_ref-Steinbuch-Weber_1974_26-0)** [Steinbuch, Karl W.](/source/Karl_W._Steinbuch); Weber, Wolfgang; Heinemann, Traute, eds. (1974) [1967]. *Taschenbuch der Informatik – Band II – Struktur und Programmierung von EDV-Systemen* (in German). Vol. 2 (3 ed.). Berlin, Germany: [Springer Verlag](/source/Springer_Verlag). [ISBN](/source/ISBN_(identifier)) [3-540-06241-6](https://en.wikipedia.org/wiki/Special:BookSources/3-540-06241-6). [LCCN](/source/LCCN_(identifier)) [73-80607](https://lccn.loc.gov/73-80607). {{[cite book](https://en.wikipedia.org/wiki/Template:Cite_book)}}: |work= ignored ([help](https://en.wikipedia.org/wiki/Help:CS1_errors#periodical_ignored))

1. **[^](#cite_ref-27)** Don Lancaster. ["TV Typewriter Cookbook"](https://www.tinaja.com/ebooks/tvtcb.pdf). ([TV Typewriter](/source/TV_Typewriter)). 1976. p. 180-181.

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