# 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 Wrens 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 set 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 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 switches and plugs and not by a stored program.[2]

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[3] contributed to its design. It has sometimes been erroneously stated that Turing designed Colossus to aid the cryptanalysis of the Enigma.[4] Turing's machine that helped decode Enigma was the electromechanical Bombe, not Colossus.[5]

The prototype, Colossus Mark 1, was shown to be working in December 1943 and was operational at Bletchley Park on 5 February 1944.[6] 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.[7] Ten Colossi were in use by the end of the war and an eleventh was being commissioned.[7] Bletchley Park's use of these machines allowed the Allies to obtain a vast amount of high-level military intelligence from intercepted radiotelegraphy messages between the German High Command (OKW) and their army commands throughout occupied Europe.

The destruction of the Colossus machines and documents, 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.[8]

## Purpose and origins

The Lorenz SZ machines had 12 wheels, each with a different number of cams (or "pins").
 Wheel number BP wheel name[9] 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. An active cam reversed the value of a bit (0→1 and 1→0).

The Colossus computers were used to help decipher intercepted radio teleprinter messages that had been encrypted using an unknown device. The British called encrypted German teleprinter traffic "Fish",[10] and the unknown machine and its intercepted messages "Tunny". Before the Germans increased the security of their operating procedures, British cryptanalysts diagnosed how the unseen machine functioned and built an imitation of it called "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 telegraph 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, a blunder by German operators 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.[11] 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.[12]

With a sufficiently 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 did this well. However, the cryptanalysts worked out that by examining the frequency distribution of the character-to-character changes in the ciphertext, instead of the plain characters, there was 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.[13] After Germany surrendered, allied forces captured a Tunny machine and discovered that it was the electromechanical Lorenz SZ (Schlüsselzusatzgerät) in-line cipher machine.[10]

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.[14] 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.[15]

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.[16] It was this task for which Colossus was initially designed. To discover the start position of the chi wheels for a message, Colossus compared two character streams, counting statistics from the evaluation of programmable Boolean functions. The two streams were the ciphertext that was read at high speed from a paper tape, and the key stream which was generated internally, in a simulation of the unknown German machine. After a succession of different Colossus runs to discover the likely chi-wheel settings, they were checked by examining the frequency distribution of the characters in processed ciphertext.[17] 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 [19] Z ciphertext D de-chi—the ciphertext with the chi component of the key removed[18] Δ any of the above XOR'ed with its successor character or bit[13] ⊕ the XOR operation[20][21] • 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".[22] 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.[23]

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.[24] 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,[17] 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.[25]

Colossus could also derive the start position of the psi and motor wheels, but this was not much done until the last few months of the war, when there were plenty of Colossi available and the number of Tunny messages had declined.

## Design and construction

Colossus 10 with its extended bedstead in Block H at Bletchley Park in the space now containing the Tunny galley of The National Museum of Computing

Colossus was developed for the "Newmanry",[26] 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.[27] 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.[28] He was recommended to Max Newman by Alan Turing who had been impressed by his work on the Bombes.[29] 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[30]

Flowers had been brought in to design the Heath Robinson's combining unit.[31] 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.[32] 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,[33] 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 to very low levels.[34] Flowers persisted with the idea and obtained support from the Director of the Research Station, W Gordon Radley.[35] Flowers and his team of some fifty people in the switching group[36][37] 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[38] 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.[39][40] It attacked its first message on 5 February 1944.[6] As it was a large structure it was quickly dubbed Colossus by the WRNS operators. This machine contained 1600 thermionic valves (tubes).[36] and was soon followed by an improved production Mark 2 machine.[41] 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.[42] 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.[32][43]

• A tape transport and an 8-photocell reading mechanism.
• Five 6-bit FIFO shift registers.
• Twelve thyratron ring stores that simulated the Lorenz machine generating a bit-stream for each wheel.
• 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.[44] 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.[45] 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.[46]

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[47] 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[48] enabled five simultaneous tests and counts to be performed giving an effective processing speed of 25,000 characters per second. [47]

## Operation

Colossus selection panel showing selections amongst others, of the far tape on the bedstead, and for input to the algorithm: ΔZ, Δ${\displaystyle \chi }$ and Δ${\displaystyle \psi }$.

The Newmanry was staffed by cryptanalysts, operators from the Women's Royal Naval Service (WRNS) – known as “Wrens” – and engineers who were permanently on hand to repair the Collosi. The first job in operating Colossus for a new message, was to prepare the paper tape loop. This was performed by the Wren operators who stuck the two ends together using Bostic, ensuring that there was a 150 character length of blank tape between the end and the start of the message.[49] Using a special hand punch they inserted a start hole between the third and fourth channels at end of the blank section, and a stop hole between the fourth and fifth channels at the end of the characters of the message.[50][51] These were read by specially positioned photocells and indicated to the processor when the message was about to start and when it ended. The operator then threaded the paper tape through the gate and around the pulleys of the bedstead and adjusted the tension. The two-tape bedstead design had been carried on from Heath Robinson so that one tape could be loaded whilst the previous one was being run. A switch on the Selection Panel specified the “near“ or the “far” tape.[52]

After performing various resetting and zeroizing tasks, the Wren operator would set the twelve wheel patterns that had been determined by the wheel breaking process and the start positions for the current run. Then, under instruction from the cryptanalyst, she would operate the “set total” decade switches and the switches and plugs to achieve the desired algorithm. She would then start the bedstead tape motor and lamp, and when the tape was up to speed operate the master start switch.[52]

## Programming

Colossus Q panel showing switches for specifying the algorithm (on the left) and the counters to be selected (on the right).

Howard Campaigne mathematician and cryptanalyst from the US Navy's OP-20-G wrote the following in a forward to Flowers'1983 paper "The Design of Colossus".

My view of Colossus was that of cryptanalyst-programmer. I told the machine to make certain calculations and counts, and after studying the results, told it to do another job. It did not remember the previous result, nor could it have acted upon it if it did. Colossus and I alternated in an interaction that sometimes achieved an analysis of an unusual German cipher system, called "Geheimschreiber" by the Germans, and "Fish" by the cryptanalysts.[53]

Colossus was not a stored program computer. The input data for the five parallel processors was read from the looped message paper tape and the electronic pattern generators for the chi, psi and motor wheels.[54] The programs for the processors were set and held on the switches and jack panel connections. Each processor could evaluate a Boolean function and count and display the number of times it yielded the specified value of "false" (0) or "true" (1) for each pass of the message tape.

Input to the processors came from two sources, the shift registers from tape reading and the thyratron rings that emulated the wheels of the Tunny machine.[55] The characters on the paper tape were called Z and the characters from the Tunny emulator were referred to by the Greek letters that Bill Tutte had given them when working out the logical structure of the machine. On the selection panel, switches specified either Z or ΔZ, either ${\displaystyle \chi }$ or Δ${\displaystyle \chi }$ and either ${\displaystyle \psi }$ or Δ${\displaystyle \psi }$ for the data to be passed to the and jack field and 'Q panel'. These signals from the wheel simulators could be specified as stepping on with each new pass of the message tape or not.

The Q panel had a group of switches on the left hand side to specify the algorithm. The switches on the right hand side selected the counter to which the result was fed. The plugboard allowed less specialized conditions to be imposed. Overall the Q panel switches and the plugboard allowed about five billion different combinations of the selected variables. [49]

As an example: a set of runs for a message tape might initially involve two chi wheels, as in Tutte's 1+2 algorithm. Such a two wheel run was called a long run, taking on average eight minutes unless the parallelism was utilised to cut the time by a factor of five. The subsequent runs might only involve setting one chi wheel, giving a short run taking about two minutes. Initially, after the initial long run, the choice of next algorithm to be tried was specified by the cryptanalyst. Experience showed, however, that decision trees for this iterative process could be produced for use by the Wren operators in a proportion of cases.[56]

## Influence and fate

Although the Colossus was the first of the electronic digital machines with programmability, albeit limited by modern standards,[57] it was not a general-purpose machine, being designed for a range of cryptanalytic tasks, most involving counting the results of evaluating Boolean algorithms.

A Colossus computer was thus not a fully Turing-complete machine. However, Professor Benjamin Wells of the Departments of Computer Science and Mathematics, University of San Francisco, has shown[58] 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. 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 and the reasons for its construction were highly secret, and remained so for 30 years after the War. Consequently it was not included in the history of computing hardware for many years, and Flowers and his associates were deprived of the recognition they were due. Colossi 1 to 10 were dismantled after the war and parts returned to the Post Office. Some parts, sanitised as to their original purpose, were taken to Max Newman's Royal Society Computing Machine Laboratory at Manchester University.[59] 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.[60]

Colossi 11 and 12 , along with two replica Tunny machines, were retained, being moved to GCHQ's new headquarters at Eastcote in April 1946, and again with GCHQ to Cheltenham between 1952 and 1954.[61] One of the Colossi, known as Colossus Blue, was dismantled in 1959; the other in 1960.[61] There had been attempts to adapt them to other purposes, with varying success; in their later years they had been used for training.[62] Jack Good related how he was the first to use Colossus after the war, persuading the US National Security Agency that it could be used to perform a function for which they were planning to build a special-purpose machine.[61] Colossus was also used to perform character counts on one-time pad tape to test for non-randomness.[61]

A small number of people who were associated with Colossus—and knew that large-scale, reliable, high-speed electronic digital computing devices were feasible—played significant roles in early computer work in the UK and probably in the US. However, being so secret, it had little direct influence on the development of later computers; it was EDVAC that was the seminal computer architecture of the time. In 1972 Herman Goldstine, who was unaware of Colossus, and its legacy to the projects of people such as Alan Turing (ACE), Max Newman (Manchester computers) and Harry Huskey (Bendix G-15) 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.[63]

Professor Brian Randell who unearthed information about Colossus in the 1970s commented on this, saying that:

It is my opinion 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.[64]

Randell's efforts started to bear fruit in the mid-1970s, after the secrecy about Bletchley Park was broken when Group Captain Winterbotham published his 1974 book The Ultra Secret.[65] In October 2000, a 500-page technical report on the Tunny cipher and its cryptanalysis—entitled General Report on Tunny[66]—was released by GCHQ to the national Public Record Office, 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.[67]

## Reconstruction

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.
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 Plug Panel. (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.[68]

Construction of a fully functional replica[69][70] of a Colossus Mark 2 was undertaken by a team led by Tony Sale.[71] 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[72] 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[73] for the event and developed his own signal processing and code-breaking code using Ada.[74] The Colossus team were hampered by their wish to use World War II radio equipment,[75] 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."[76]

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."[77]

## 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. ^
3. ^ See Banburismus
4. ^ Golden, Frederic (29 March 1999), "Who Built The First Computer?", Time Magazine, vol. 153 no. 12
5. ^ Copeland, Jack, Colossus: The first large scale electronic computer, retrieved 21 October 2012
6. ^ a b Copeland 2006, Copeland, Jack, Machine against Machine p. 75.
7. ^ a b Flowers 1983, p. 246.
8. ^ The National Museum of Computing: The Colossus Gallery, retrieved 18 October 2012
9. ^ Good, Michie & Timms 1945, 1 Introduction: 11 German Tunny, 11B The Tunny Cipher Machine, p. 6.
10. ^ a b Good, Michie & Timms 1945, 1 Introduction: 11 German Tunny, 11A Fish Machines, (c) The German Ciphered Teleprinter, p. 4.
11. ^ Copeland 2006, Budianski, Stephen Colossus, Codebreaking and the Digital Age pp. 55-56.
12. ^ Copeland 2006, Tutte, William T. My Work at Bletchley Park p. 357.
13. ^ a b Good, Michie & Timms 1945, 1 Introduction: 11 German Tunny, 11C Wheel Patterns, (b) Differenced and Undifferenced Wheels, p. 11.
14. ^ Copeland 2006, Copeland, Jack, Turingery pp. 378–385.
15. ^ Good, Michie & Timms 1945, 24 - Rectangling: 24B Making and Entering Rectangles pp. 114-115, 119-120.
16. ^ Good, Michie & Timms 1945, 1 Introduction: 11 German Tunny, 11E The Tunny Network, (b) Wheel-breaking and Setting, p. 15.
17. ^ a b Small 1944, p. 15.
18. ^ a b Good, Michie & Timms 1945, 1 Introduction: 12 Cryptographic Aspects, 12A The Problem, (a) Formulae and Notation, p. 16.
19. ^ Good, Michie & Timms 1945, 1 Introduction: 11 German Tunny, 11B The Tunny Cipher Machine, (e) Psi-key, p. 7.
20. ^ The Boolean or "truth" function XOR, also known as Exclusive disjunction and Exclusive or, is the same as binary modulo 2 addition and subtraction
21. ^ Good, Michie & Timms 1945, 1 Introduction: 11 German Tunny, 11B The Tunny Cipher Machine, (a) Addition, p. 5.
22. ^ Copeland 2006, Budiansky, Stephen, Colossus, Codebreaking, and the Digital Age pp. 58–59.
23. ^ Carter 2008, pp. 18-19.
24. ^ Small 1944, p. 65.
25. ^ Roberts 2009, 34 minutes in.
26. ^ Good, Michie & Timms 1945, 3 Organisation: 31 Mr Newman's section, p. 276.
27. ^ Anderson 2007, p. 8.
28. ^ Randell 1980, p. 9.
29. ^ Budiansky 2000, p. 314.
30. ^ Exhibit in the National Cryptologic Museum, Fort Meade, Maryland, USA
31. ^ Good, Michie & Timms 1945, 1 Introduction: 15 Some Historical Notes, 15A First Stages in Machine Development, (c) Heath Robinson, p. 33.
32. ^ a b Copeland 2006, Flowers, Thomas H. Colossus p. 96.
33. ^ Flowers 1983, p. 244.
34. ^ Copeland 2006, Copeland, Jack, Machine against Machine p. 72.
35. ^ Copeland 2006, Copeland, Jack, Machine against Machine p. 74.
36. ^ a b Copeland 2006, Flowers, Thomas H. Colossus p. 80.
37. ^ Copeland 2006, Randell, Brian Of Men and Machines p. 143.
38. ^
39. ^ The Colossus Rebuild http://www.tnmoc.org/colossus-rebuild-story
40. ^
41. ^ Good, Michie & Timms 1945, 1 Introduction: 15 - Some Historical Notes, 15C Period of Expansion, (b) Colossus, p. 35.
42. ^ Randell, Brian; Fensom, Harry; Milne, Frank A. (15 March 1995), "Obituary: Allen Coombs", The Independent, London, retrieved 18 October 2012
43. ^ Flowers 1983, pp. 249-252.
44. ^ Flowers 1983, pp. 243, 245.
45. ^
46. ^ 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.
47. ^ a b Copeland 2006, Flowers, Thomas H. Colossus p. 100.
48. ^ This would now be called a systolic array
49. ^ a b Good, Michie & Timms 1945, 5 Machines: 53 Colossus 53A Introduction, p.333.
50. ^ Good, Michie & Timms 1945, 5 Machines: 53 Colossus 53B The Z stream, p.333.
51. ^ Flowers 1983, pp. 241,242.
52. ^ a b Fensom 2006, p. 303.
53. ^ Flowers 1983, pp. 239–252.
54. ^ Small 1944, p. 108.
55. ^ Good, Michie & Timms 1945, 5 Machines: 53 Colossus, pp. 333-353.
56. ^ Budiansky 2006, p. 62.
57. ^ A Brief History of Computing. Jack Copeland, June 2000
58. ^ 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.
59. ^ "A Brief History of Computing". alanturing.net. Retrieved 26 January 2010.
60. ^ McKay 2010, pp. 270–271.
61. ^ a b c d Copeland 2006, Copeland, Jack, et al. Mr Newman's section pp. 173–175.
62. ^
63. ^ Goldstine 1980, p. 321.
64. ^ Randell 1980, p. 87.
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