# Colossus computer

Not to be confused with the fictional computer of the same name in the movie Colossus: The Forbin Project.
Developer A Colossus Mark 2 computer being operated by Dorothy Du Boisson (left) and Elsie Booker. The slanted control panel on the left was used to set the "pin" (or "cam") patterns of the Lorenz. The "bedstead" paper tape transport is on the right. Tommy Flowers assisted by Sidney Broadhurst, William Chandler and for the Mark 2 machines, Allen Coombs Post Office Research Station Special-purpose electronic digital programmable computer First-generation computer Mk 1: December 1943; Mk 2: 1 June 1944 8 June 1945 10 Electric typewriter output Programmed, using switches and plug panels Custom circuits using thermionic valves and Thyratrons. A total of 1600 in Mk 1 and 2400 in Mk 2. Also relays and stepping switches None (no RAM) Indicator lamp panel Paper tape of up to 20 000 × 5-bit characters in a continuous loop 7.5 kW[citation needed]

Colossus was the name of a series of computers developed by British codebreakers in 1943-1945 to help in the cryptanalysis of the Lorenz cipher. Colossus used thermionic valves (vacuum tubes) and thyratrons to perform Boolean and counting operations. Colossus is thus regarded[1] as the world's first programmable, electronic, digital computer, although it was programmed by plugs and switches and not by a stored program.

Colossus was designed by research telephone engineer Tommy Flowers to solve a problem posed by mathematician Max Newman at the Government Code and Cypher School (GC&CS) at Bletchley Park. Alan Turing's use of probability in cryptanalysis[2] contributed to its design. It has sometimes been erroneously stated that Turing designed Colossus to aid the cryptanalysis of the Enigma.[3] Turing's machine that helped decode Enigma was the electromechanical Bombe, not Colossus.[4]

The prototype, Colossus Mark 1, was shown to be working in December 1943 and was operational at Bletchley Park on 5 February 1944.[5] An improved Colossus Mark 2 that used shift registers to quintuple the processing speed, first worked on 1 June 1944, just in time for the Normandy Landings on D-Day.[6] Ten Colossi were in use by the end of the war and an eleventh was being commissioned.[6] Bletchley Park's use of these machines allowed the Allies to obtain a vast amount of high-level military intelligence from radiotelegraphy messages between the German High Command (OKW) and their army commands throughout occupied Europe.

The destruction of the Colossus hardware and blueprints, as part of the effort to maintain a project secrecy that was kept up into the 1970s, deprived most of those involved with Colossus of credit for their pioneering advancements in electronic digital computing during their lifetimes. A functioning replica of a Colossus computer was completed in 2007 and is on display at The National Museum of Computing at Bletchley Park.[7]

## Purpose and origins

The Lorenz SZ machines had 12 wheels, each with a different number of cams (or "pins").
 Wheel number BP wheel name[8] Number of cams (pins) 1 2 3 4 5 6 7 8 9 10 11 12 ${\displaystyle \psi }$1 ${\displaystyle \psi }$2 ${\displaystyle \psi }$3 ${\displaystyle \psi }$4 ${\displaystyle \psi }$5 ${\displaystyle \mu }$37 ${\displaystyle \mu }$61 ${\displaystyle \chi }$1 ${\displaystyle \chi }$2 ${\displaystyle \chi }$3 ${\displaystyle \chi }$4 ${\displaystyle \chi }$5 43 47 51 53 59 37 61 41 31 29 26 23
Cams on wheels 9 and 10 showing their raised (active) and lowered (inactive) positions.

The Colossus computers were used to help decipher radio teleprinter messages that had been encrypted using an unknown device. The British called encrypted German teleprinter traffic "Fish",[9] and the unknown machine and its intercepted messages "Tunny". Before the Germans increased the security of their operating procedures, British cryptanalysts diagnosed how the machine functioned and built a machine that emulated it, ("British Tunny").

It was deduced that the machine had twelve wheels and used a Vernam ciphering technique on message characters in the standard 5-bit ITA2 code. It did this by combining the plaintext characters with a stream of key characters using the XOR Boolean function to produce the ciphertext.

In August 1941, an operating blunder led to the transmission of two versions of the same message with identical machine settings. These were intercepted and worked on at Bletchley Park. First, John Tiltman, a very talented GC&CS cryptanalyst derived a key stream of almost 4000 characters.[10] Then Bill Tutte, a newly arrived member of the Research Section, used this key stream to work out the logical structure of the Lorenz machine. He deduced that the twelve wheels consisted of two groups of five, which he named the χ (chi) and ψ (psi) wheels, the remaining two he called μ (mu) or "motor" wheels. The chi wheels stepped regularly with each letter that was encrypted, while the psi wheels stepped irregularly, under the control of the motor wheels.[11]

With a truly random key stream, a Vernam cipher removes the natural language property of a plaintext message of having an uneven frequency distribution of the different characters, to produce a uniform distribution in the ciphertext. The Tunny machine worked well in this respect, but the cryptanalysts worked out that examining the character-to-character changes of character streams, instead of the frequency distribution of ciphertext characters, showed a departure from uniformity which provided a way into the system. This was achieved by "differencing" in which each bit or character was XOR-ed with its successor.[12] After Germany surrendered, allied forces captured a Tunny machine and discovered that it was the electromechanical Lorenz SZ (Schlüsselzusatzgerät) in-line cipher machine.[9]

In order to decrypt the transmitted messages, two tasks had to be performed. The first was "wheel breaking", which was the discovery of the cam patterns for all the wheels. These patterns were set up on the Lorenz machine and then used for a fixed period of time for a succession of different messages. Each transmission, which often contained more than one message, was enciphered with a different start position of the wheels. Alan Turing invented a method of wheel-breaking that became known as Turingery.[13] Turing's technique was further developed into "Rectangling" for which Colossus could produce tables for manual analysis. Colossi 2, 4, 6, 7 and 9 had a "gadget" to aid this process.[14]

The second task was "wheel setting", which worked out the start positions of the wheels for a particular message, and could only be attempted once the cam patterns were known.[15] It was this task for which Colossus was initially designed, to discover the start position of the chi wheels for a message. To do this it compared two character streams, counting statistics based on a succession of programmable Boolean functions. The two streams were the ciphertext which was read at high speed from a paper tape, and the key stream which was generated internally, in a simulation of the Lorenz machine. After a succession of different Colossus runs, the putative chi-wheel settings were checked by examining the frequency distribution of the characters in processed ciphertext, which were essential in checking the settings that had been found.[16] Colossus produced these frequency counts.

## Decryption processes

 P plaintext K key – the sequence of characters XOR'ed (added) to the plaintext to give the ciphertext ${\displaystyle \chi }$ chi component of key ${\displaystyle \psi }$ psi component of key ${\displaystyle \psi '}$ extended psi – the actual sequence of characters added by the psi wheels, including those when they do not advance [18] Z ciphertext D de-chi—the ciphertext with the chi component of the key removed[17] Δ any of the above XOR'ed with its successor character or bit[12] ⊕ the XOR operation[19][20] • Bletchley Park shorthand for telegraphy code space (zero) x Bletchley Park shorthand for telegraphy code mark (one)

By using differencing and knowing that the psi wheels did not advance with each character, Tutte worked out that trying just two differenced bits (impulses) of the chi-stream against the differenced ciphertext would produce a statistic that was non-random. This became known as Tutte's "1+2 break in".[21] It involved calculating the following Boolean function:

∆Z1 ⊕ ∆Z2 ⊕ ∆${\displaystyle \chi }$1 ⊕ ∆${\displaystyle \chi }$2 =

and counting the number of times it yielded "false" (zero). If this number exceeded a pre-defined threshold value known as the "set total", it was printed out. The cryptanalyst would examine the printout to determine which of the putative start positions was most likely to be the correct one for the chi-1 and chi-2 wheels.[22]

This technique would then be applied to other pairs of, or single, impulses to determine the likely start position of all five chi wheels. From this, the de-chi (D) of a ciphertext could be obtained, from which the psi component could be removed by manual methods.[23] If the frequency distribution of characters in the de-chi version of the ciphertext was within certain bounds, "wheel setting" of the chi wheels was considered to have been achieved,[16] and the message settings and de-chi were passed to the "Testery". This was the section at Bletchley Park led by Major Ralph Tester where the bulk of the decrypting work was done by manual and linguistic methods.[24]

Colossus could also derive the start position of the psi and motor wheels, but this was not much done until latterly when there were plenty of Colossi available.

## Design and construction

In 1994, a team led by Tony Sale (right) began a reconstruction of a Colossus at Bletchley Park. Here, in 2006, Sale supervises the breaking of an enciphered message with the completed machine.

Colossus was developed for the "Newmanry",[25] the section headed by the mathematician Max Newman that was responsible for machine methods against the Lorenz machine. The Colossus design arose out of a prior project that produced a counting machine dubbed "Heath Robinson". The main problems with Heath Robinson were the relative slowness of electro-mechanical parts and the difficulty of synchronising two paper tapes, one punched with the enciphered message, and the other representing the key stream of the Lorenz machine.[26] Heath Robinson tapes tended to stretch when being read, at some 2000 characters per second, resulting in unreliable answers.

Tommy Flowers was a senior electrical engineer and Head of the Switching Group at the Post Office Research Station at Dollis Hill who had been appointed MBE in June 1943. Prior to his work on Colossus, he had been involved with GC&CS at Bletchley Park from February 1941 in an attempt to improve the Bombes that were used in the Cryptanalysis of the German Enigma cipher machine.[27] He was recommended to Max Newman by Alan Turing who had been impressed by his work on the Bombes.[28] The main components of Colossus's predecessor, Heath Robinson were as follows.

Stepping switch from an original Colossus presented by the Director of GCHQ to the Director of the NSA to mark the 40th anniversary of the UKUSA Agreement in 1986[29]

Flowers had been brought in to design the Heath Robinson's combining unit.[30] He was not impressed by the system of a key tape that had to be kept synchronised with the message tape and, on his own initiative, he designed an electronic machine which eliminated the need for the key tape by having an electronic analogue of the Lorenz (Tunny) machine.[31] He presented this design to Max Newman in February 1943, but the idea that the one to two thousand thermionic valves (vacuum tubes and thyratrons) proposed, could work together reliably, was greeted with great scepticism,[32] so more Robinsons were ordered from Dollis Hill. Flowers, however, knew from his pre-war work that most thermionic valve failures occurred as a result of the thermal stresses at power up, so not powering a machine down reduced failure rates very substantially.[33] Flowers persisted with the idea and obtained support from the Director of the Research Station, W Gordon Radley.[34] Flowers and his team of some fifty people in the switching group[35][36] spent eleven months from early February 1943 designing and building a machine that dispensed with the second tape of the Heath Robinson, by generating the wheel patterns electronically.

This prototype, Mark 1 Colossus, performed satisfactorily at Dollis Hill on 8 December 1943[37] and was taken apart and shipped to Bletchley Park, where it was delivered on 18 January and re-assembled by Harry Fensom and Don Horwood.[38][39] It attacked its first message on 5 February 1944.[5] As it was a large structure it was quickly dubbed Colossus by the WRNS operators. This machine contained 1600 thermionic valves (tubes).[35] and was soon followed by an improved production Mark 2 machine.[40] Nine of this version of the machine were constructed, the first being commissioned on 1 June 1944, after which Allen Coombs took over leadership of Colossus production.[41] The original Mark 1 machine was converted into a Mark 2 and an eleventh Colossus was essentially finished when the war in Europe ended.

The main units of the Mark 2 design were as follows.[31][42]

• A tape transport and an 8-photocell reading mechanism.
• A set of five 6-bit FIFO shift registers.
• Twelve bit-stream generating thyratron ring stores that simulated the Lorenz machine.
• Panels of switches for specifying the program and the "set total".
• A set of function units that performed Boolean operations.
• A "span counter" that could suspend counting for part of the tape.
• A master control that handled clocking, start and stop signals, counter readout and printing.
• Five electronic counters.
• An electric typewriter.

Most of the design of the electronics was the work of Tommy Flowers, assisted by William Chandler, Sidney Broadhurst and Allen Coombs; and Erie Speight and Arnold Lynch developing the photoelectric reading mechanism.[43] Coombs remembered Flowers, having produced a rough draft of his design, tearing it into pieces that he handed out to his colleagues for them to do the detailed design and get their team to manufacture it.[44] Work on the Mark 2 design started while Mark 1 was being constructed. It contained 2400 valves and was both 5 times faster and simpler to operate than the original version.[45]

The design overcame the problem of synchronizing the electronics with the message tape by generating a clock signal from the reading of the sprocket holes of the message tape. The speed of operation was thus limited by the mechanics of reading the tape. The tape reader was tested up to 9700 characters per second (53 mph) before the tape disintegrated. So 5000 characters/second (40 ft/s (12.2 m/s; 27.3 mph)) was settled on as the speed for regular use.

Flowers designed shift registers[46] one for each of the five channels of the punched tape. For each circuit of the tape, the shift register stored successive bits from each of the tape channels and delivered five successive characters (either Z or ΔZ according to switch selection) to the processors. The five-way parallelism[47] enabled five simultaneous tests and counts to be performed giving an effective processing speed of 25,000 characters per second. [46]

## Operation

Colossus used state-of-the-art vacuum tubes (thermionic valves), thyratrons and photomultipliers to optically read a paper tape and then applied programmable logical functions to the bits of the key and ciphertext characters, counting how often the function returned "false".

Colossus was designed to perform the task of "Wheel Setting", that is determining the start point of the stream of key characters in relation to the characters of the enciphered message on the paper tape loop. Initially it was only the χ (chi) wheels that were examined. To keep the size of the task manageable, only two bits of the chi-stream were examined in the first run,[48] then progressively the other bits.[49] Success at this stage allowed the production of a version of the ciphertext from which the chi component of the key had been removed, the so-called "de-chi". This transformation allowed manual methods to be used to work out the settings of the ψ (psi) and μ mu "motor" wheels.

Later, methods were devised for using Colossus to determine the settings of the psi wheels. All of this required that "wheel breaking", the discovery of the cam patterns for all the wheels, had been successfully achieved. Later Mark 2 Colossi were equipped with a special unit to achieve this as well. Programming Colossus was by setting switches and plugging appropriate units together. Sometimes, two or more Colossus computers tried different possibilities simultaneously in what is now called parallel computing, speeding the decoding process by perhaps as much as double the rate of comparison.[citation needed]

## Influence and fate

Colossus was the first of the electronic digital machines with programmability, albeit limited by modern standards.[50]

• It had no internally stored programs. To set it up for a new task, the operator had to set up plugs and switches to alter the wiring.
• Colossus was not a general-purpose machine, being designed for a specific cryptanalytic task involving counting and Boolean operations.

A Colossus computer was thus not a fully general Turing-complete machine. However, Professor Benjamin Wells of the Departments of Computer Science and Mathematics, University of San Francisco, has shown[51] that a Universal Turing Machine could have been run on the set of ten Colossus computers. This means that Colossus satisfies the definition of Turing completeness. Most of the other computing machines of this era were also not Turing complete (e.g. the Atanasoff–Berry Computer, the Bell Labs relay machines (by George Stibitz et al.), or the first designs of Konrad Zuse).[citation needed] The notion of a computer as a general purpose machine—that is, as more than a calculator devoted to solving difficult but specific problems—did not become prominent until after World War II.

Colossus was preceded by several computers, many of them first in some category. Zuse's Z3 was the first functional fully program-controlled computer, and was based on electromechanical relays, as were the (less advanced) Bell Labs machines of the late 1930s (George Stibitz, et al.). The Atanasoff–Berry Computer was electronic and binary (digital) but not programmable. Assorted analog computers were semi-programmable; some of these much predated the 1930s (e.g., Vannevar Bush). Babbage's Analytical Engine design predated all these (in the mid-19th century), it was a decimal, programmable, entirely mechanical construction—but was only partially designed and never built during Babbage's lifetime. Colossus was the first combining digital, (partially) programmable, and electronic. The first fully programmable digital electronic computer was the ENIAC which was completed in 1946.

The use to which the Colossus computers were put was of the highest secrecy, and the Colossus itself was highly secret, and remained so for many years after the War. Thus, it could not be included in the history of computing hardware for many years, and Flowers and his associates were deprived of the recognition they were due.

Being not widely known, Colossus had little direct influence on the development of later computers; it was EDVAC that was the early design which had the most influence on subsequent computer architecture. However, the technology of Colossus, and the knowledge that reliable high-speed electronic digital computing devices were feasible, did have a significant influence on the development of some early computers in the United Kingdom and probably in the US. A number of people who were associated with the project and knew all about Colossus played significant roles in early computer work in the UK. In 1972, Herman Goldstine wrote that:

Britain had such vitality that it could immediately after the war embark on so many well-conceived and well-executed projects in the computer field.[52]

In writing that, Goldstine was unaware of Colossus, and its legacy to those projects of people such as Alan Turing (with the Pilot ACE and ACE), and Max Newman and I. J. Good (with the Manchester Mark 1 and other early Manchester computers). Brian Randell later wrote that:

the COLOSSUS project was an important source of this vitality, one that has been largely unappreciated, as has the significance of its places in the chronology of the invention of the digital computer.[53]

Colossus documentation and hardware were classified from the moment of their creation and remained so after the War. Tommy Flowers was ordered to destroy all documentation and burnt them in a furnace at Dollis Hill. He later said of that order:

That was a terrible mistake. I was instructed to destroy all the records, which I did. I took all the drawings and the plans and all the information about Colossus on paper and put it in the boiler fire. And saw it burn.[54]

Some parts, sanitised as to their original use, were taken to Newman's Royal Society Computing Machine Laboratory at Manchester University.[55] Most of the Colossus computers were dismantled and parts returned to the Post Office. Two, along with two replica Tunny machines, were retained, moving to GCHQ's new headquarters at Eastcote in April 1946, and moving again with GCHQ to Cheltenham between 1952 and 1954.[56] One of the Colossi, known as Colossus Blue, was dismantled in 1959; the other in 1960.[56] There had been attempts to adapt them to other purposes, with varying success; in their later years they had been used for training.[57] Jack Good relates how he was the first to use it after the war, persuading the NSA that Colossus could be used to perform a function for which they were planning to build a special-purpose machine.[56] Colossus was also used to perform character counts on one-time pad tape to test for non-randomness.[56]

For nearly three decades after the war Colossus remained secret, long after any of its technical details were of any importance. The need for such secrecy ebbed away as communications moved to digital transmission and all-digital encryption systems became common in the 1960s. Information about Colossus began to emerge publicly in the 1970s, after the secrecy imposed was broken when Group Captain Winterbotham published his 1974 book The Ultra Secret. More recently, a 500-page technical report on the Tunny cipher and its cryptanalysis – entitled General Report on Tunny – was released by GCHQ to the national Public Record Office in October 2000; the complete report is available online,[58] and it contains a fascinating paean to Colossus by the cryptographers who worked with it:

It is regretted that it is not possible to give an adequate idea of the fascination of a Colossus at work; its sheer bulk and apparent complexity; the fantastic speed of thin paper tape round the glittering pulleys; the childish pleasure of not-not, span, print main header and other gadgets; the wizardry of purely mechanical decoding letter by letter (one novice thought she was being hoaxed); the uncanny action of the typewriter in printing the correct scores without and beyond human aid; the stepping of the display; periods of eager expectation culminating in the sudden appearance of the longed-for score; and the strange rhythms characterizing every type of run: the stately break-in, the erratic short run, the regularity of wheel-breaking, the stolid rectangle interrupted by the wild leaps of the carriage-return, the frantic chatter of a motor run, even the ludicrous frenzy of hosts of bogus scores.[59]

## Reconstruction

Front view of the Colossus rebuild showing, from right to left (1) The "bedstead" containing the message tape in its continuous loop and with a second one loaded. (2) The J-rack containing the selection panel and jack field. (3) The K-rack with the large "Q" switch panel and sloping patch panel. (4) The double S-rack containing the control panel and, above the image of a postage stamp, five two-line counter displays. (5) The electric typewriter in front of the five sets of four "set total" decade switches in the C-rack.[60]
Rear view of the two bays of the Colossus rebuild, showing many of the 2400 vacuum tubes and thyratrons used.

Construction of a fully functional replica[61][62] of a Colossus Mark 2 was undertaken by a team led by Tony Sale.[63] In spite of the blueprints and hardware being destroyed, a surprising amount of material survived, mainly in engineers' notebooks, but a considerable amount of it in the U.S. The optical tape reader might have posed the biggest problem, but Dr. Arnold Lynch, its original designer, was able to redesign it to his own original specification. The reconstruction is on display, in the historically correct place for Colossus No. 9, at The National Museum of Computing, in H Block Bletchley Park in Milton Keynes, Buckinghamshire.

In November 2007, to celebrate the project completion and to mark the start of a fundraising initiative for The National Museum of Computing, a Cipher Challenge[64] pitted the rebuilt Colossus against radio amateurs worldwide in being first to receive and decode three messages enciphered using the Lorenz SZ42 and transmitted from radio station DL0HNF in the Heinz Nixdorf MuseumsForum computer museum. The challenge was easily won by radio amateur Joachim Schüth, who had carefully prepared[65] for the event and developed his own signal processing and code-breaking code using Ada.[66] The Colossus team were hampered by their wish to use World War II radio equipment,[67] delaying them by a day because of poor reception conditions. Nevertheless, the victor's 1.4 GHz laptop, running his own code, took less than a minute to find the settings for all 12 wheels. The German codebreaker said: "My laptop digested ciphertext at a speed of 1.2 million characters per second—240 times faster than Colossus. If you scale the CPU frequency by that factor, you get an equivalent clock of 5.8 MHz for Colossus. That is a remarkable speed for a computer built in 1944."[68]

The Cipher Challenge verified the successful completion of the rebuild project. "On the strength of today's performance Colossus is as good as it was six decades ago", commented Tony Sale. "We are delighted to have produced a fitting tribute to the people who worked at Bletchley Park and whose brainpower devised these fantastic machines which broke these ciphers and shortened the war by many months."[69]

## Other meanings

There was a fictional computer named Colossus in the 1970 movie Colossus: The Forbin Project. This was sheer coincidence as it pre-dates the public release of information about Colossus, or even its name.

Neal Stephenson's novel Cryptonomicon (1999) also contains a fictional treatment of the historical role played by Turing and Bletchley Park.

## Footnotes

1. ^ Copeland 2006, Copeland, Jack, Introduction p. 2.
2. ^ See Banburismus
3. ^ Golden, Frederic (29 March 1999), "Who Built The First Computer?", Time Magazine, vol. 153 no. 12
4. ^ Copeland, Jack, Colossus: The first large scale electronic computer, retrieved 21 October 2012
5. ^ a b Copeland 2006, Copeland, Jack, Machine against Machine p. 75.
6. ^ a b Flowers 1983, p. 246.
7. ^ The National Museum of Computing: The Colossus Gallery, retrieved 18 October 2012
8. ^ Good, Michie & Timms 1945, 1 Introduction: 11 German Tunny, 11B The Tunny Cipher Machine, p. 6.
9. ^ a b Good, Michie & Timms 1945, 1 Introduction: 11 German Tunny, 11A Fish Machines, (c) The German Ciphered Teleprinter, p. 4.
10. ^ Copeland 2006, Budianski, Stephen Colossus, Codebreaking and the Digital Age pp. 55-56.
11. ^ Copeland 2006, Tutte, William T. My Work at Bletchley Park p. 357.
12. ^ a b Good, Michie & Timms 1945, 1 Introduction: 11 German Tunny, 11C Wheel Patterns, (b) Differenced and Undifferenced Wheels, p. 11.
13. ^ Copeland 2006, Copeland, Jack, Turingery pp. 378–385.
14. ^ Good, Michie & Timms 1945, 24 - Rectangling: 24B Making and Entering Rectangles pp. 114-115, 119-120.
15. ^ Good, Michie & Timms 1945, 1 Introduction: 11 German Tunny, 11E The Tunny Network, (b) Wheel-breaking and Setting, p. 15.
16. ^ a b Small 1944, p. 15.
17. ^ a b Good, Michie & Timms 1945, 1 Introduction: 12 Cryptographic Aspects, 12A The Problem, (a) Formulae and Notation, p. 16.
18. ^ Good, Michie & Timms 1945, 1 Introduction: 11 German Tunny, 11B The Tunny Cipher Machine, (e) Psi-key, p. 7.
19. ^ The Boolean or "truth" function XOR, also known as Exclusive disjunction and Exclusive or, is the same as binary modulo 2 addition and subtraction
20. ^ Good, Michie & Timms 1945, 1 Introduction: 11 German Tunny, 11B The Tunny Cipher Machine, (a) Addition, p. 5.
21. ^ Copeland 2006, Budiansky, Stephen, Colossus, Codebreaking, and the Digital Age pp. 58–59.
22. ^ Carter 2008, pp. 18-19.
23. ^ Small 1944, p. 65.
24. ^ Roberts 2009, 34 minutes in.
25. ^ Good, Michie & Timms 1945, 3 Organisation: 31 Mr Newman's section, p. 276.
26. ^ Anderson 2007, p. 8.
27. ^ Randell 1980, p. 9.
28. ^ Budiansky 2000, p. 314.
29. ^ Exhibit in the National Cryptologic Museum, Fort Meade, Maryland, USA
30. ^ Good, Michie & Timms 1945, 1 Introduction: 15 Some Historical Notes, 15A First Stages in Machine Development, (c) Heath Robinson, p. 33.
31. ^ a b Copeland 2006, Flowers, Thomas H. Colossus p. 96.
32. ^ Flowers 1983, p. 244.
33. ^ Copeland 2006, Copeland, Jack, Machine against Machine p. 72.
34. ^ Copeland 2006, Copeland, Jack, Machine against Machine p. 74.
35. ^ a b Copeland 2006, Flowers, Thomas H. Colossus p. 80.
36. ^ Copeland 2006, Randell, Brian Of Men and Machines p. 143.
37. ^
38. ^ The Colossus Rebuild http://www.tnmoc.org/colossus-rebuild-story
39. ^
40. ^ Good, Michie & Timms 1945, 1 Introduction: 15 - Some Historical Notes, 15C Period of Expansion, (b) Colossus, p. 35.
41. ^ Randell, Brian; Fensom, Harry; Milne, Frank A. (15 March 1995), "Obituary: Allen Coombs", The Independent, London, retrieved 18 October 2012
42. ^ Flowers 1983, pp. 249-252.
43. ^ Flowers 1983, pp. 243, 245.
44. ^
45. ^ For comparison, later stored-program computers such as the Manchester Mark 1 of 1949 used 4050 valves, Lavington, S. H. (July 1977), "The Manchester Mark 1 and Atlas: a Historical Perspective" (PDF), Communications of the ACM - Special issue on computer architecture, 21 (1): 4–12, doi:10.1145/359327.359331, retrieved 8 February 2009 while ENIAC (1946) used 17,468 valves.
46. ^ a b Copeland 2006, Flowers, Thomas H. Colossus p. 100.
47. ^ This would now be called a systolic array
48. ^ Small1944, p. 19.
49. ^ Small 1944, p. 20.
50. ^ A Brief History of Computing. Jack Copeland, June 2000
51. ^ Wells, Benjamin (2009). "Proceedings of the 8th International Conference on Unconventional Computation 2009 (UC09), Ponta Delgada, Portugal: Advances in I/O, Speedup, and Universality on Colossus, an Unconventional Computer". Lecture Notes in Computer Science. Berlin, Heidelberg: Springer-Verlag. 5175: 247–261. ISBN 978-3-642-03744-3. Retrieved 2009-11-10.
52. ^ Goldstine 1980, p. 321.
53. ^ Randell 1980, p. 87.
54. ^ McKay 2010, pp. 270–271.
55. ^ "A Brief History of Computing". alanturing.net. Retrieved 26 January 2010.
56. ^ a b c d Copeland 2006, Copeland, Jack, et al. Mr Newman's section pp. 173–175.
57. ^
58. ^
59. ^ Good, Michie & Timms 1945, 5 Machines
51 Introductory, (j) Impressions of Colossus, p. 327.
60. ^
61. ^ The Colossus Gallery, The National Museum of Computing, retrieved 30 March 2015
62. ^ "The Colossus Rebuild Project – by Tony Sale". Retrieved 30 October 2011
63. ^ Colossus - The Rebuild Story, The National Museum of Computing, retrieved 30 March 2015
64. ^ "Cipher Challenge". Archived from the original on 1 August 2008. Retrieved 1 February 2012.
65. ^
66. ^
67. ^ Ward, Mark (16 November 2007). "BBC News Article". Retrieved 2 January 2010.
68. ^
69. ^ "Latest Cipher Challenge News 16.11.2007". Archived from the original on 2008-04-18.