Talk:Gray code

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Baudot
Can Baudot's use of reflected binary codes be explained, or even verified? What I find in sources don't show any Gray-like code, nor how we might have used them. Dicklyon (talk) 01:33, 19 December 2020 (UTC)

I mean, I can see that if you sort his codewords in Gray-code order, the vowels come out first, in alphabetical order, then a few things and the consonants in order. Presumably there's a reason for that. But what? I can't see a relationship between how Baudot codes were used and the properties of Gray codes. And I can't find a source that mentions it. Anyone? Dicklyon (talk) 03:16, 21 December 2020 (UTC)


 * (edit-conflict) Hi Dick, I have meanwhile added many references describing this in better details. I'm still trying to dig deeper in the history to find answers to a few of my own open questions, but regarding your question, what I found in the sources so far is that this particular arrangement was chosen to make it easier for the operator to memorize the patterns, and possibly also to make it easy to enter the chords. The synchronous Baudot telegraph used a chorded keyboard and the operator's input had to be manually kept in sync with the machine while keying in the chords, so this was very timing-sensitive.
 * One source also mentioned that the codes were arranged in order of frequency, but this is wrong (the later Murray code was arranged this way, but not the 5-level Baudot code).
 * --Matthiaspaul (talk) 23:46, 21 December 2020 (UTC)
 * What sources say such things? My impression was that it was more about the scanning machine's teeth, nothing to do with the operator. Dicklyon (talk) 04:25, 22 December 2020 (UTC)

I trimmed that section down. I couldn't find anything in sources to suggest the Mimault's telegraph used a Gray-like code and there was a bunch of text and excess refs unrelated to Gray code. Baudot and his code have their own articles. Dicklyon (talk) 23:36, 21 December 2020 (UTC)

Could you be so kind as to explain how the material you added back helps understand how the Gray code was used? Can you explain how it was used and why it mattered? Is there a sourced explanation we can incorporate, or just the somewhat cryptic French one? Dicklyon (talk) 20:18, 22 December 2020 (UTC)

That section on telegraphy remains cryptic and uninterpretable, and has now been bloated up with fancy tables that don't help at all. Why/how do the properties of a Gray code become relevant in that context? I'd delete the section if no relevance can be shown. Dicklyon (talk) 05:33, 29 December 2020 (UTC)
 * Huh? The section is top relevant here per the sources because it documents the usage of what we now call Gray code or reflected binary code long before Stibitz and Gray, and even by two people independent of each other, Schäffler and Baudot (both in the telegraphy business). Schäffler's usage can be traced down to a telegraph he produced in 1874 (and Lambert claimed to have shown him this code in 1872). Baudot's usage can be traced down to a telegraph he built in 1875/1876 (many sources attribute this to his 1874 patent, but the prototype documented there still used a 6-level rather than a 5-level code). Baudot's research on this started in 1872 as well. (Mimault - at his time unsuccessfully - claimed priority on some aspects of Baudot's telegraph, including the code, so this would deserve at least being mentioned for NPOV.)
 * The 1872 date is relevant because it coincidentally matches the date when Gros described his "baguenodier".
 * The Schäffler and Baudot code tables clearly show that they actually used codes very similar to Gray's. Some of the modern sources (even top RS ones) actually call them "Gray codes".
 * Like you I want to find answers as to why they used these codes because this is historically interesting, but the question if this belongs here or not is already answered by the fact that they used these codes, not why.
 * It is relevant to describe the codes as fixed-length 5-level codes - ideally, we would avoid the term 5-bit, as some authors do, because this is long before Shannon's introduction of bits, and even the idea of binary codes was new and terminology non-established (that's why some of the historical descriptions are what you call "cryptic" - they weren't in the context of their times).
 * As I mentioned already, the Baudot multiplexing telegraph was still a synchronous telegraph and it used a chorded keyboard. The operator's input had to be manually kept in sync with the machine while keying in the chords, which was very timing-sensitive.
 * These timing constraints could have been one of the reason(s) for why the code was arranged the way it was.
 * What I also found in the sources is that the code was arranged to be easy to type and remember for the operator. I don't know if this was the primary goal or a by-product of the timing constraints. Either case, it certainly contributed to reducing the error rate and increasing the speed an operator was able to key in the chords while keeping in sync with the machine.
 * --Matthiaspaul (talk) 14:40, 30 December 2020 (UTC)
 * I think it is wild speculation to associate the choice of a Gray-like code with the telegraph being multiplexed, or synchronous, or having a chorded keyboard. If anything, sources suggest maybe some internal scanning order of matching the inputs, which is itself unrelated to the code-letter ordering.  Different tables use different codes, sometimes Gray-like and sometimes not.  So I think it best to say that some sources have recognized Gray-like codes in some of Baudots machines, rather than to put all the stuff that is only speculatively related. Dicklyon (talk) 05:37, 6 January 2021 (UTC)
 * And what is the point of the "Plan of 5-level signals" table? And what is the point of the Schäffler table that doesn't even associate the codes with letters or anything meaningful?  Are they just there as pretty pictures, or is there something we can learn from them relevant to Gray codes? Dicklyon (talk) 05:42, 6 January 2021 (UTC)
 * From the Zemanek ref, it seems clear that, in Schäffler's case at least, the reflected binary code was part of the printer's internal scanning order; there's no necessary connection from there to the ordering of characters in the printer or the assignment of codes to characters, except that they have to be consistent. This makes good sense.  Saying that Baudot used reflected binary in his code makes much less sense; did  he have a printer with characters in that order, and so decided to assign the codes that way?  And who first observed that Baudot used a reflected binary code?  I've ordered a copy of the Knuth volume that has this, but that seems to be 2005, and it came into our article in 2002, so I still wonder from where. Dicklyon (talk) 05:44, 24 January 2021 (UTC)
 * And the Moncel ref goes into detail on Baudot's "combinateur" which lays out the symbols with Gray code, to control the scanning recognition for printing, as in Schäffler's machine. Too bad it's in French; can anyone translate the juicy bits for us? I'm pretty sure it's still just an internal detail, not related in any significant way to what codes go with what letters.  More about printing than about telegraphy, really. Dicklyon (talk) 06:48, 24 January 2021 (UTC)

Moncel translation
I OCR'd, corrected, and had translated the Moncel ref. Lots of interesting details in there, including a section on the alphabet, but no clue about any Gray-code-like properties. The key bit where it could have been mentioned is here: The characters of the type wheel do not follow each other on this wheel in alphabetical order, but in the following order: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 A É E I O U Y B C D F G H J ... If you look at the codes corresponding to this order, they are the reflected-binary codes. The reason for choosing such a code is that they are laid out consecutively in that order on a wheel with 5 contacts, and they don't want more than one transition, potentially causing a glitch, in going from one position to the next as the wheel turns. Some of the other sources imply that, but this one really doesn't. I'm going to remove it.

My point is, the Gray code is not about the assignment of codes to letters. It's about the internal ordering of the characters on the printing wheel. More to do with printing than with telegraphy, and nothing to do with multiplex or with the keyboard; synchronous, yes, if one character is printed per wheel revolution and it turns at a constant speed.

Feel free to hat/hide this if you know how: Dicklyon (talk) 00:03, 25 January 2021 (UTC)

Multiple transmission printing telegraph systems and elementary signal combinations by M. Th. du MONCEL. (Continuation and end.) M. Baudot's system. We have seen by what series of combinations and reasoning Mr. Mimault had been led to his system telegraphic printer, who was first (in 1874) electro-chemical and 5-wire, then electromagnetic and one-wire, by its application to the Hughes device and its combination with the Meyer system. Point The start of Mr. Baudot's system was different. At the time he has was designed, there was much concern about the telegraph at multiple transmissions from Mr. Meyer who had given excellent results, and M. Baudot sought whether there would be no way of applying the principle of this system at Hughes' printing telegraph, in used for some time on the main lines of Europe. But this idea was difficult to realize, precisely because of the unequal spacing of the prints which could vary from 1 time up to 28 times, without there being any way to regularize it, since the type wheel in this telegraph runs at a perfectly uniform way. It is certain that if by some means mechanical we had been able to carry out impressions after the same space of time and to ensure that the letter Z, for example, which is the last of the alphabet, could happen in front of the printing mechanism as fast as the letter B, we would have been able to devote a determined time to this function which would have been still the same, and the signal preparation time could have be used for other transmissions made by other devices, as in the Meyer system. But this problem that had preoccupied as early as 1848 Mr. Highton, though difficult to resolve, had did not frighten M. Baudot, because in 1872 he had combined a system telegraph in which functions of this kind were obtained. He had in fact succeeded by means of such a printer four-wheeled types, progressively advancing relative to each other to the other, to obtain the printing in Roman characters of the different letters transmitted according to the Morse vocabulary. In this system, current emissions corresponding to lines moved longitudinally the wheels on their axis, so as to bring either one or the other of these wheels above paper, and the emissions which corresponded to points, rotated this axis, different quantities depending on whether one or more the other of the wheels was above the paper. By modifying this system a little, M. Baudot was quick to make it better able to meet the demands of the problem it had posed, in reducing to one the wheels of the types and reacting on its motor axis three electromagnets which, by means of three wheels ratchet of different diameters, could turn it one greater or lesser quantity. The action of these three electromagnets depended on a kind of rheotome governed by two electromagnets interposed in the line circuit and reacting, one to place this or that of the three first electromagnets in the circuit of a fairly strong local battery to determine the rotation of the corresponding ratchet wheel, the other to close this circuit under the influence of an inversion of the current of line succeeding the first programs produced. However for obtain the stop of the type wheel when passing the character designated before the printing mechanism, it was necessary that movements of the three ratchet wheels which controlled the walk were exact multiples of each other, and that these multiple were such that the combined and repeated movements of these wheels could make the wheel of the types take the 28 positions necessary for printing the different characters of the alphabet. However, this result could be obtained in a fairly simple way by arranging these wheels so that, for a single action produced by the 3 electromagnets, their movement was in the ratio of numbers 1, 3, 9; because by producing two successive emissions of the line current, each wheel could increase the stroke of the wheel of types from single to double, and one could obtain by combination of these 6 movements 26 different positions of this wheel, which could suffice for the immediate printing of alphabetic characters. Nevertheless like movements too extended from the wheel of current types and reversals in unequal numbers were to cause some inconvenience, Mr. Baudot preferred to increase the number of original broadcasts of the current as well as that of the electromagnets called to react on the different ratchet wheels, and by bringing this number to 6, it was found leads to arranging them in such a way as to provide movements proportional to the numbers 1, 2, 4, 8, 16, 32, which allowed him to obtain 63 combinations without using each time more than one current reversal. Still he thought to delete this one by subjecting the rheotomes, at both stations, to a movement synchronic. He then reduced the number of electromagnets to 5, rightly thinking that the 31 combinations they could provide were quite sufficient. At the time when M. Baudot dealt with the provision we have just come to exhibit, that is to say in 1873, his apparatus did not yet resolve the problem we talked about at the start. It was, like those of MM. Highton, Mimault, Whitehouse, a telegraph at independent impression which could not theoretically present advantages that because a character, to be printed, had no need to wait for all those placed before him in order alphabetical had passed. There was still a long way to go to the application from the multiple system to the Hughes, and moreover these movements progressive wheel types could result in large implementation difficulties. It is By seeking an intermediary less delicate in its functions and especially less complicated between the wheel types and electromagnets called to designate the signals that M. Baudot was led to the ingenious device to which he gave the name of combiner, and which enabled it, by making it a device waiting for transmitted signals, to make use of the systems telegraphic synchronous motion printers, and to use to other transmissions the time intervals which could exist between the formation of signals on this waiting device and their impression. It was in 1875 that this important invention was patented, and it constitutes, by its very object, a very marked between the system of M. Baudot. and those of MM. Highton, Whitehouse and Mimault who had preceded. As for the use of electro-mechanical functions on the rise geometric in the combiner in question, we have seen how M. Baudot had been successively taken there; But regardless of construction considerations that may have put on the way, and without having recourse either to Pascal's triangle or to the theory of algebraic combinations, it was enough for him to relate to the well-known 5-needle Wheatstone telegraph, to find out than with 5 signal elements combined two to two, three to three, four to four, etc., he could get 31 likely combinations to represent the letters of the alphabet and the most used signals in telegraphy, and as by means of distributing apparatus placed at both ends of the line he could make react the currents transmitted on the electro-magnetic organs called to providing the elementary signals, the problem of transmission direct all alphabetic signals to the dialer are was thus solved in a fairly simple manner, without requiring like the 5-wire Wheatstone telegraph. Here is now how M. Baudot realized the advantages of this telegraphic arrangement to the point of view of the speed of transmissions. If in a time t, we can transmit a single signal, we can, in a double time 2t, and by the intervention of the distributor who will have enabled a new signal, transmit three different signals, two of which will be isolated and one resulting from the combination. In a triple time 3t and with a new signal element in addition supplied by the distributor, we will be able to transmit 3 singly and 4 in combination, in all 7. In a quadruple time 4t, the number of these different signals can thus rise to 15, and in a fivefold time 5t, we can choose between 31 different signals corresponding to the different letters of the alphabet. During this time 5t, the most complicated signal can therefore be reproduced. Now, assuming that each permutation line wire on the distributors is done at the same time as that from one letter to another on the printer, we could prepare on this one the printing of such letter that one would like while the wheel of the types would have carried out only the 5/28 of its revolution. However, since it takes some time to prepare a signal, it must admit that part of the revolution of this wheel is used in this preparation, and M. Baudot paid him a quarter of its circumference. The other three quarters therefore correspond to the 28 alphabetical signals, and if we assume that this wheel of types does as in the Hughes two revolutions per second, each distributor contacts corresponding to a type of the wheel in question will have a duration represented by (0 ", 5) / (28 + 9) or 0", 0135 (0.0135 s), and this duration is more than sufficient, since, according to experiments with the Hughes apparatus, it was recognized that the t necessary for the transmission of a signal on a line of 500 kilometers does not exceed 0 ", 003. However, starting from this duration 0 ", 0135, we find that the distributor, running synchronously with the wheels of the types, could perform 7 multiple transmissions during each revolution of these wheels1), which are transmitted multiple could therefore cause the impression of 7 letters, on 7 receivers, in half a second, i.e. 840 letters per minute or 504 dispatches of 20 words per hour. If we increased the speed of distributors and receivers to the point of not attributing transmissions that a duration of 0 ", 003, the output could be increased to over a thousand dispatches per hour. These calculations, however, do should be considered as purely theoretical, and, in the practice, it is hardly necessary to count on a yield nel to the number of multiple transmissions that can be established. Now in M. Baudot's apparatus this number does not exceed 5, and in admitting that with the Hughes one can transmit a letter and half a turn, with the Baudot device only one yield increase in the ratio of 5 to 1.5, i.e. a little more than three times. Experience has shown, moreover, that send 300 dispatches per hour in this way on a 800 kil. 1) Each letter requiring 5 successive contacts of 0 ", 0135 or one total duration of 0 ", 0675, each turn of the distributor carried out in 0", 5 can only activate a number of receivers represented by the ratio of 0 ", 5 to 0", 0675. Now this number is 7.407. By separating the series of 5 contacts by an interval equivalent to one contact, or not could only have 6 multiple transmissions. From this preamble, we see that the Baudot system, like remain those of MM. Highton, Whitehouse, Mimault, features four different kinds of devices: manipulators, receivers, intermediate waiting devices, or combiners, and a distributor general whose function is not only to put successively the line in relation to each of the systems telegraphs, but also to have a single line wire produced effects that would determine a line of 5 threads. We are going to study successively these various Organs; but, first, we must say that these devices are arranged for five transmissions multiple and that, like those of the Meyer telegraph, the different systems which compose them are established on the same table, ' which is arranged to allow 5 employees to be conveniently installed on its sides. For this purpose, this table carries on each of these sides three advanced parts on which are fixed the devices specific to each transmission, and the employees are placed in the re-entrant parts. The middle of the table is occupied by the driving devices, the distributor and the shaft intended for provide movement to all receivers; we can see some, figure 9, the layout for one of the receivers. Manipulator . —Each of the manipulators who is represented seen by above, figure 8, consists of a five-key keypad or for better to say of a vertical board AB behind which are articulated five Morse keys, three on the right, two on the left, which are arranged one above the other so that fingers of both hands can easily react to the levers that finish them. These keys press, on the side opposite to the lever and by via a spring, on a common metal rod K which keeps them in a fixed position; they are from elsewhere trimmed on both sides of the lever, below the lever itself, of four spring forks F, F which each rub on two blades, one of which is continuous and the other cut in two, this which constitutes, for each key, a quadruple switch. This complicated arrangement was adopted to ensure, as in Mr. Wheatstone's rapid telegraph, that the broadcasts of currents can be positive and negative, and that those following to programs already produced in the same direction, can be find performed under an electrical influence of less energy than those produced for the first time or those which follow reverse emissions. Figure 11 shows the electrical arrangements of these switches and their connection mode with the distributor, which is shown in part developed on a flat surface to the left of the figure. But before talking about these connections, it is important that we say a few words in the way how the various devices are connected and how is arranged * the distributor itself; we will therefore have to refer to figure 9. We have already seen that in this system all the receivers are put in movement by the same motor shaft. This tree is in hh, and its movement is provided by a fairly powerful clockwork mechanism which does not need great precision, because it is, as it is will see later, electrically adjusted with each revolution of the motor shaft. The same is not true of a second M placed at the other end of the table and which sets the Machine set in D . Not only must it be regularized by means of a vibrating blade, as in the Hughes apparatus, but the distributor itself must still be provided with a double mechanism corrector in order to make it work completely synchronously with that of the corresponding station, and subject to this synchronism the operation of the receivers it governs. To achieve this double effect, the distributor's mobile system G carries a sort of box of gearing V which we will discuss at the moment and by means of which he can have his movement suspended for a time more or less short when it is ahead of its correspondent. On the other hand, the motor shaft hh which turns the receivers E , crosses the axis m 'of the distributor's mobile system, so as to rotate concentrically with it while maintaining movement completely independent. With this arrangement, we understand that it suffices to adapt to this tree hh a ZZ ebonite disc fitted with a metal contact, so that a particular wiper is carried by the mobile system G of the distributor, can react electrically to a brake adapted to the motor mechanism of the shaft, and slow down its movement at each turn of it, if it happens, like that by the way must take place since this mechanism has no moderator, that this movement tends to take more and more speed. We will study this device later, but to finish with the links of different. devices between them, we must add that each receiver B is accompanied by a combiner C, and that these combiners are both connected to the distributors D of the two corresponding stations and receiver mechanisms to which they correspond. This connection is purely electrical in the first case; but it is both mechanical and electrical in the second, because if the electromagnets of these combiners perform the circuit combinations that must provide the different signals, a working mechanical system must be agree with the wheel of the corresponding receiver types, may, by meeting the contacts related to these combinations, determine a local electrical action capable of operating the printing mechanism of the receiver. We are now going study in detail these different organs and we will start naturally by distributors. Distributor . - The distributor, in M. Baudot's system, is a slightly more complicated than in the Meyer system, because it has five parallel rows of contacts distributed around the circumference of two ebonite drums D, d (fig. 9) of different diameters, and one of these rows q4, arranged on a particular disc whose circumference follows the surface of the drum, is likely to be moved circularly to adjust the devices according to the length of telegraph lines. The contacts of the first three rows g4, q5, q6, arranged on the largest drum and the following disc, are distributed for each of these rows in six series having six contacts each, except the last one which has only four; this is reserved for the correction which we will see later mode of action, and the other five correspond to the five systems telegraphs intended to provide multiple transmission. Their contacts are consequently connected, for one of the rows, to the manipulators, and for the other rows to combiners and receptors of each of these systems; however, one of these contacts, the last in each series, is connected directly to the pole negative of the line stack and only plays a passive role, as will see right away. The last two rows of contacts q1, q3, which are fixed on the small drum d and which are nothing more than two rings divided into six equal parts, are intended to connect to the line through the distributor's trotters the contacts of the first row and second row, depending on whether a switch is set the disposition of each employee arranges the line for the transmission or reception. Figure 11 shows the development of these contacts and their mode of liaison with different parts of the device. The contacts of the first row of the large drum match in series to the five manipulators and are individually connected to each of the keys of the corresponding manipulator; so these are transmission contacts. Those in the second row are the receiving contacts and correspond like the first ones, by series, to the five combiners, while being individually connected to the five electromagnets that are part of each of these combinators. Finally the contacts of the third row still communicate in series, both with the electromagnets of local combiners through the receiving contacts to which they are connected by a U-shaped slider, which presses on both rows, and with the manipulators, by one of the switches of the keys we will call local switch . It is through the contacts of this third row that dispatches are printed at the start and that the combiners are brought back to their position normal before they are brought into play again (see Figure 11). Above the distributor which is fixed, except the part corresponding to the first row of contacts, support the changeover springs, which are seven in number. Five correspond to the five rows of contacts we talked about, and the sixth, which is precisely the U-spring mentioned at the moment, precedes the others, in their walk, a distance equal to the length of one of the contacts. These springs are attached to a VG rotating arm, fig. 9, put moving by a hollow axis m ' depending on the mechanism clockwork regularized M and through which passes as we have seen the end of the horizontal shaft hh which controls the movement of receivers. However, this movement is only communicated to this arm. via the gearbox already discussed and which is none other than a ratchet wheel V to which it is connected by a strong ratchet with several teeth. This ratchet, represented in large, in 0, figure 10, with its accessories, reacts on the opposite side on a rocker fitted with an ankle c which, at each revolution of the arm G carrying the springs, passes over an articulated lever Ip the end of which is terminated by an inclined plane p. This lever is engaged on an electromagnetic trigger i (figure 9), adapted to the armature a of a particular electromagnet e, and this electromagnet is related with distributor correction contacts. Now it follows from this mechanism, a constantly renewed correction that maintains the movements of the movable arms of the two distributors in correspondence in a state of perfect synchronism. Indeed the ankle position c, fig. 10, of the clutch pawl in the two distributors is such that when the movements are perfectly synchronized, this peg, on both devices, at the same time arrives at the beginning of the inclined plane p of the lever engaged; but precisely at this moment the trotters of the distributors arrived at both stations on the contacts of correction we talked about, and since these contacts are related to the corrective solenoid and, they can transmit the current to through it and release the engaged lever lp . Therefore the ratchet clutch can pass over the inclined plane p of this lever without disengaging the motor mechanism of the walkers. If at on the contrary, one of the movements is faster than the other, the contact which causes the corrective electromagnet to react is not carried out on the device walking faster than after the wise step of the pawl c on the lever engaged I p, and this then disengages this pawl which does not can re-engage only after having crossed the inclined plane p ; it naturally results in a small delay in the walking of the supporting arm trotters, and this delay may be enough to understand the greatest speed with which it was animated. This action is also ensured by a second articulated lever r, which presses on the inclined plane i? and below which engages the ankle c . Since the electromagnet e is a Hughes electromagnet, its armature a must be put back into position and this function is carried out at the same time as the reconnection of the mechanism, by the action of two eccentrics b and f, fig. 9, who react on it by means of two levers l and g, the action of one ahead of the other a little. As the contacts related to the second row of the distributor cannot correspond, in position, to those of the first row, since the effect produced cannot be achieved at the same time of arrival and departure, and that this lack of correspondence is more or less accentuated depending on the length of the line, it is necessary, in order to bring these contacts to an agreement between them, to settle the reciprocal position of the two discs which carry them, and it is for that the first, q4 is likely to move on its axis. This movement is carried out using a pinion wrench K, figure 9, engaged in a window adapted to the movable disc and one of which edges, parallel to its circumference, is provided with a small rack. By means of this system, the trotters of the two distributors in connections therefore pass at the same time at both stations on the corresponding contacts of each series and can, therefore way, successively establish the junction by the line, different keys of each manipulator with the electromagnets of the corresponding combiner. Only, as the action is successive, it is necessary that these electromagnets maintain their frame in the position made by the current that has passed through them, so that this action by combining with one or more others in the combiner, can provide the signal desired. It is for this reason that we had to use polarized armature electromagnets. Combiner . - The combiner is composed, like the distributor, a fixed part and a moving part and in addition to a system electromagnetic composed of the five electromagnets of which we have spoken, and which acts like a multiple relay system double contacts. Figure 11 gives a representation theoretical. The fixed part consists of five double metal discs with notched circular rim, arranged in such a way that the void practiced in one of the ledges is almost filled with a protruding part cut in the rim of the juxtaposed disc. These two parts of each disc are isolated from each other, such that the circumference which they form externally is composed of parts which may be unequal in length, but which are isolated from each other and which alternately belong to two different discs, capable of being electrically connected with different circuits. All of these double discs, however, are provided at a point of their circumference, which is the same for all, and over an arc of about 80 degrees, with a very large notch filled with an insulating material, which leaves the device inactive for about a quarter of a revolution of its moving part, and it is precisely during this time that employees prepare their signal to manipulators. In figure 11, we assume the rings formed by these different double disc systems, developed in a straight line, and for distinguish from each other the parts belonging to each disc coupled, one reached them, the ones in black, the others in White. As these black and white parts are, by the fact, only isolated contacts connected to the contacts of the armatures of the five electromagnets of the electromagnetic system, we distinguish from each other by calling black the contacts indicated in black, and white contacts not tinted. That put us will examine how these different series of contacts with respect to each other. The bottom AAA ring, etc. (fig. 11), which we will designate under the No.5. Door, as seen, 8 black contacts and 8 white contacts of the same length, except the last of white which is only half others. If we assume the metal part of these disks divided into 31 equal parts, each of the black and white contacts of this fifth ring would correspond to 2 divisions, except the last of the whites who would only understand one. The fourth ring does not carry 4 black contacts and 5 white contacts which each correspond to 4 divisions, except the last two which are white and do not include that one and two divisions. They are placed in relation to the contacts of the fifth ring, so that the contacts black start and end in the middle of each of the black contacts of this fifth ring. The third ring carries only two black contacts and three white contacts, and these black contacts, like previously, are arranged to start and end at middle of two consecutive black contacts of the fourth ring, this which causes that the two white contacts which are at the ends include only 3 and 4 divisions, while the others in include 8. The second ring has only one black contact left and two white contacts which include the first 16 divisions, the seconds 8 and 7 divisions, and always commits the black contact and ends in the middle of the two black contacts of the third ring. Finally the first ring has only a black contact and a white contact, the the first comprising 16 visions, the last 15. The black contact then begins at one end of the indentation and ends at middle of the contact of the same type of the second ring. If we carefully consider the reciprocal arrangement of these various contacts, it is immediately recognized that, thanks to this arrangement, five springs R1 R2 R3 R4 R5 placed in a straight line and which would revolve around these 5 rings, can never meet at the same time two separations of black and white contacts, and by therefore the functions of each of them are clearly determined to complement the closures of the local circuit at through the printing mechanism. The various black and white contacts of these rings are also connected by wires to the double contacts A, B, C, D, E of the 5 electromagnets of the combiner which it has previously discussed and which constitute what we call the electro-magnetic rheotome. This binding is made of such that the white contacts correspond to the contacts under which the reinforcement rests in normal times, and that the black contacts correspond to the upper contacts on which support these frames when they are deflected. In examining the position of this or that of the reinforcements a, &, c, d, e on can easily, according to this explanation, find the open ways through the combiner. The electro-magnetic system is moreover nothing more than five Siemens polarized electromagnets, whose armature oscillates between two stops forming the previous contacts A, B, C, D, E, and found maintained in the last position it occupied, by result of its polarity and the remanent magnetism of the electromagnet. These reinforcements being the switching members intended to put in action the printing mechanism, are naturally related to this mechanism and the local battery P, the circuit of which must be completed by the combiner; but as they can act more or less large number, they must, with the different rings of the combiner, be an integral part of a continuous circuit closed by the mobile system of the combiner and, therefore, be linked between both of them, except the one that communicates directly to the pile P. It is for this reason that reinforcements b and c , d and e are metallically united as seen in the figure. The mobile part of the combiner is composed, like that of the distributor, of a series of 5 spring trotters R1, R2, R3, R4, R5, suitable for an arm mounted on the axle of the type wheel and which turns with it, and like the 31 characters on this wheel correspond exactly to the 31 divisions according to which were established the contacts of the combiner, these springs pass successively before these different divisions at the same time as the different characters of the type wheel pass in front of the printing mechanism. Consequently, if the type wheel is suitably placed in relation to this trotter system, we can ensure that by the time this system reaches the tenth or the fifteenth division of the combiner, for example, the tenth or the fifteenth letter is placed in position to be printed. The mobile system of the combiner being the counterpart of the system electro-magnetic and having to complete the circuit whose path is prepared by this last system, must have its trotters connected two to two, like the armatures of electromagnets; only this connection must be made in an opposite way, so that the current transmitted circulates meandering through the five rings of the combiner. Also it is the springs R4 and R3, R2 and R1 which are connected together, and it is the fifth Rs that communicates with the battery P via the printing electromagnet I. With this arrangement, it is easy to see how the current of the pile P is closed at each turn of the trotters and according to the action determined on one or another of the electromagnets. Indeed, suppose that the lower keys of the corresponding manipulator have deflects, through the distributors, the reinforcements e and c of the combiner: the current leaving the battery P will be directed by the armature which has not moved on the white contacts of the fifth ring of the combiner, and as to get out it must pass through a white contact of the fourth ring, a black contact of the third, a white contact of the second and a black contact of the first, it cannot be find in these conditions that when the trotters will have arrived at the twenty-fourth division; then the circuit crossed will be as follows: armature a, 6th white contact of the 5th ring, res out R1, spring R2, 4D white contact of 4th ring, armature b, armature c deflected, 2nd black contact of 3rd ring, spring R3, spring R4, 2nd white contact of the second ring, armature of the armature deviated, black contact of the first ring, R5 spring, printing electromagnet, battery. The printing mechanism then being brought into play, prints the letter in this moment at hand, and this letter is the twenty-fourth of the wheel of types. We will see later that this letter is the S. We now understand, from the functions that we come from to analyze, which will be possible by the different combination of positions of the electromagnetic rheostome armatures, combination carried out under the influence of the manipulators and by through the distributors, not to obtain the closure of the current local printer that at the very moment when the letter of the types, designated by this combination, arrives in front of the mechanism printer. M. Baudot imagined still other simpler combinators in their construction which have the advantage of being able to operate mechanically the printing mechanism, and consequently without local current. In these combiners, the fixed part of the device is mobile, and reciprocally the mobile part constituted by the springs walkers is fixed. These springs are in fact replaced by species of articulated rockers which carry fixed normally close of their axis of the arms pressing on a lever depending on the system first impression. Five Hughes electromagnets, in connection with the distributor, are placed in front of one of the ends of these rockers so that their frame, when detached, can tilt them and consequently release their arm from the printing lever. Above the opposite end of these rockers, is the mechanism combinator proper which is arranged much like the one that we have studied previously, but which, instead of contacts different in nature, has alternately hollow parts and protruding arranged, moreover, like these contacts. This cylinder, as we said at the beginning, turns with the wheel of types of the printer, and, in this movement, provokes naturally the lowering of the rockers that the protruding parts meet; so that when the turn of this cylinder has been accomplished, all these rockers had to be lowered, either mechanically by the combiner, or electrically by the electromagnets. Then the printing mechanism is released and can produce the impression, but this impression can be done more or sooner depending on the position and number of lowered scales electrically, because the combiner only completes the action thus produced, and this complement is only carried out when the position of this combiner corresponds to the arrival of the letter transmitted in front of the printing mechanism. This one is loaded then, after printing the letter, take care to re-enter all the scales and put all the reinforcements back at the same time deviated from the electromagnets in contact with them. This system, as is easily understood, could still be electrically combined. It would suffice for this to keep at 5 combinator electromagnets the arrangement we have studied in the first place, and to consider the rockers from which it comes to be a question of scull switches oscillating between two contacts and with an idle contact. By connecting these double contacts to those of electromagnets, and by metallic flip-flops two by two in an inverse manner to that of the reinforcements of these, one of the switch systems can serve as complement to the other, and the combinator cylinder by carrying out required this complement, determines the impression by launching the local current through the printing electromagnet. We win at this system the elimination of the 5 trotter springs, and the construction of Combiner cylinder is much simpler, since there is no longer any isolated contacts or double discs. M. Baudot now gives preference for these two systems; but as it is the first who has been executed so far, we had to stop there longer. Receiver . - The receptors in this system look like much to the part of the Hughes Telegraph which constitutes the printing mechanism; a type T wheel, figures 9 and 12, whose characters occupy only three quarters of the circumference; a printing wheel 0 provided with 32 pointed teeth in the part of its circumference corresponding to the types of the preceding wheel and which is mounted on the same axle of this wheel; a mechanism for permutation of numbers and letters; a printing system I, J, x, x put into action under the influence of a trigger electromagnetic; such are the various parts which compose it. This printing system, however, does not work as in the Hughes apparatus; the axis with the four cams not being there, printing is done under the influence of the motor which sets in motion the types wheel and combiner, and through the wheel of 32 teeth 0 which was discussed previously. This indeed has for function, when the J armature of the electromagnet is detached, to lead an arm Ha; fixed on the articulation axis of this frame, which is currently within reach of its teeth; and as this one is equipped with a system of rollers NH ## on which the paper strip is rolled up, this strip can be pressed against the T-type wheel. This roller system consists of the remainder of two small guide cylinders xx around which the strip of paper, and an NH rolling mill system, one of the cylinders, mounted on the axis of the frame itself, carries the snap PP 'intended to advance the paper. It's easy to understand, moreover, that the wheel of 32 teeth O which thus governs the impression can, being provided with a permutation mechanism similar to that which is suitable for the correcting wheel of Hughes devices, determine printing letters or numbers when the arm H x ; wearing the rollers meet, between the teeth of this wheel, the appendix system which activates this mechanism. To obtain that after each printing the reinforcement of the electromagnet is mechanically replaced in contact with its poles, Mr. Baudot establishes on the support of the mechanism a rocker with spring L which, being met by a peg I adapted to the wheel 32 teeth O, can be tilted far enough back when passing through the indented part of this wheel, to make the arm travel impression H #, in the opposite direction of its first movement, the arc circle he had described under the influence of the trigger electro-magnetic and the drive produced by the O wheel. The result is that the armature J is again brought into contact with the electromagnet I, and therefore able to provide new action. Linking devices to each other. - Now that we have described the way in which the organs of the manipulators of the distributors, combiners and receivers, we will to be able to study more easily their mode of connection, and we let's start with the manipulators first. We have seen that these devices were each equipped with four switches having the form shown, fig. 13, where only two are figured. These switches each consist of a spring inverted U rubbing on three contacts, one which is long and which corresponds more or less directly to the distributor's contacts, the other two which are short and which also correspond more or less directly to both poles of the line stack. In fig. 11, which represents all the connections of the devices, these four switches are indicated only by their contacts, and it is necessary to admit consequently that there exist above them the trotters in U of which we have just spoken, which bring together in long contact, depending on whether the button is raised or lowered, the upper contact or the bottom contact. In this figure, only the switches related to three of the keys of a manipulator, the connections being always the same for the other keys. Over there same reason, only part of the distributor's contacts have been shown, and these contacts are shown on the left at the top of the figure. The trotter springs of this distributor are indicated in r, r1 r2, r3, r4, and the direction of their movement as well as that of the springs R1, R2, R3, R4, R5 of the combiner is indicated by arrows. The + and - signs indicate that the contacts to which they belong are placed in direct contact with the two poles of the line stack, and these same signs surmounted by the letter R indicate that a resistance has been introduced through the communication wires of this battery to reduce the voltage. From the inspection of the figure, we first see that the first switches of each key are set by their long contacts in report with the plates of the local distributor, and only receive the current, except that of the first key, only through the second and third switches of the preceding key, which communicate to it, depending on whether the transmissions are made with currents succeeding each other in the same direction or in opposite directions, more or less strong electric charges. It is precisely these variable loads that keep the line at the same potential and realize the benefits Mr. Wheatstone has achieved in his fast telegraph with the compensating currents. Let us indeed follow the course of the currents in a transmission made using keys 3 and 4 down. Unweakened positive current will be first directed to the third distributor contact; because the line is already under the influence of a negative charge that it still has in normal times, and this current transmitted by the third key comes through the third switch of the second key not lowered. Immediately afterwards, a new positive current is sent to the distributor's fourth contact by the fourth key lowered but it is weakened, because it does not reach the first switch of this key only through the third switch of the third key which is then lowered and whose second contact is related to the weakened pole of the battery. As by the time this current crosses the line, it is already loaded positively, it therefore only needs a weak positive charge to take back the potential it must have to function regularly. If instead of lowering keys 3 and 4, we had lowered keys 2 and 4, it would not have been the same: a first current positive non-weakened would have been transmitted by the second touch to the second distributor contact in the same way as that previously transmitted by the third key, but the one that would have transmitted the fourth touch would not have been weakened, because the third key not having been lowered, the current would have arrived at the first switch of the fourth key by the first contact of the third switch of the third key, and this current not weakened would have been essential to reverse the load weakened negative that the line would have acquired under the influence of this third key not lowered. It remains for us to discuss the functions of the fourth switch of each key, functions that are double, because this switch is used both for local impressions and recall to their position normal of the electromagnetic armatures of the combiner. As for the others, the two contacts of this switch are connected to the two poles of a battery; but this stack is a local stack, and each long contacts of these switches is connected to a contact of the third row of distributor. Normally, this long contact being connected to that of the switch contacts related to the negative pole of the local battery, it happens that when the manipulator does not not working, all the contacts of the third row of the distributor are negatively charged, and therefore when the small spring, in U of the distributor (the one that precedes the others) comes to pass over these contacts, it successively transmits this load to the receiving contacts who, transmitting it in turn to electromagnets of the local combiner, through them determine the closure of five negative currents. Now these negative currents then recall to their normal position those of the reinforcements of these electromagnets which would have been deflected in the previous turn of the distributor, and as the action of the U-shaped trotter precedes that of the other wipers, the combiner is placed in position to provide new combinations before the passage of these. Of a on the other hand, and for the same reason, when the manipulator is put in game, the distributor contacts in relation to the keys lowered are positively charged and operate the electromagnets of the same local combiner, which therefore determines printing of the dispatch at the outgoing post and before it is transmitted to the receiving station. Under these conditions, only one switch may be sufficient, because the circuit, being local, is not subjected to effects of load variations which influence both transmissions across the lines. Alphabetical system . - Figure 14 below shows the alphabetical system adopted by M. Baudot. The different signals that can be done with the right and left keys are indicated by small circles placed in squares, and these signals being arranged like the numbers to be combined in a table of multiplication, we can see, by following the leagues horizontally and vertically, what is the letter designated by each combination signals. This table is double to match the two wheel positions of types which provide printing of letters and that of numbers. This is how we see that the letter corresponding to a simple lowering of key N ° 1 of the right manipulator is' A, that lowering the first right key and the first key on the left give the J, that the three keys on the right and the two keys on the left lowered give the P, that the isolated lowering of the two keys of left gives the white letters or the numbers, etc. We must however note that the order of the keys on these tables must be interpreted, in relation to that indicated on the fig. 11, as if the two keys on the left represented the keys 1 and 2, and as if the three keys on the right represent keys 5, 4 and 3, keys 2 and 5 being indicated plots which correspond to indexes. If we follow on the combiner the numbers of the divisions to which the various combinations indicated in these tables, it is recognized that the letters that they designate do not correspond to their rank in the order alphabetical. This is due to what M. Baudot wanted, as in the Morse alphabet, apply the simplest combinations to most frequently repeated letters in dispatches. The characters of the type wheel do not follow each other on this wheel in alphabetical order, but in the following order: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 A É EIOUYBCDFGHJ White numbers 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 KLMNPQRSTVWXZ t Blac letters Operation of devices . - Now it's time to see how all these devices work, and we'll assume that it is the third manipulator of station A which is put in action to transmit the letter H to station B. The employee of station A will then lower the first two buttons of the right manipulator and the second from the left manipulator. Depending on the arrangement of the devices, these lowered keys will be those we have designated in fig. 11 under the numbers 2, 4, 5. This reduction will be carried out during the passage of the resorts walkers in front of the insulating part of the distributors that we suppose to walk synchronously. When these springs will reach the third series of contacts of these distributors, the line will be put in contact, by contacts N ° 2 of this one with the reinforced positive pole stinks a line and that by key N ° 2. The positive current arriving through the second contact of the distributor of the station B to the second electromagnet of the third combiner, will tilt its armature d on the contact in relation to the black contact of the second ring of the combiner. Almost at the same time the keys 4 and 5 of the manipulator will transmit through contacts 4 and 5 distributors of equally positive currents that will cross the electromagnets 4 and 5, and will bear their armatures a and b on the contacts corresponding to the black contacts of rings 4 and 5 of the combiner. However, the positive charges thus transmitted do not will not be the same, because button 3 is not lowered, the positive charge which will be transmitted to button 4 will be reinforced, while it will be weakened for key 5 due to lowering of button 4 which preceded it. So we will find ourselves in the case of good transmission, and the three reinforcements a , b , d deviated will open to the local current, when the trotters of the combinator will come to pass, the following way: deflected armature a , fourth black contact of the fifth ring of the combiner, spring R1, spring R2, second black contact of the fourth ring, deflected armature b, armature c , second white contact of the third ring, spring R3, spring R4, black contact of the second ring, deflected armature d, armature e , white contact of the first ring, spring R5, battery. But that will only be when the trotters are arrived in front of the thirteenth division that this current will be completed. Gold this thirteenth division corresponds precisely to the letter H. It is easy to understand that the same effects being reproduced on electromagnets of the local combiner of station A which transmits, the letter H will be found in the same way printed under the influence of fourth switch of the three down keys. Ultimately, we see that, by this system, all letters of the alphabet and numbers can be printed under the influence of five keys that are held constantly under the fingers, and that we lower in such or such order as is appropriate to re present the 31 letters and signs of the alphabet. Without doubt this impression is not made instantly at the time of transmission, but the time separating successive impressions is regularized, and can be used for other transmissions, which are carried out successively in the same order and which quintuple the number of dispatches sent and received. This device was built with great skill by Mr. Dumoulin-Froment, the son-in-law and successor of the illustrious builder M. Froment, and as I have already said, the first tests were very satisfactory. It is hoped that this system can be advantageously applied in practice. Postscript . —As a result of an error by the copyist certain sentences from the previous article that had been erased in pencil on my manuscript, have been reproduced and suggest that the first M. Mimault's system was likely to apply to the multiple transmission; but as we could see by the last one paragraph of this article and the preliminary account of the system, it does not is not so. This system could have no other result than to print directly and independently of each other the different alphabetic characters, as did the rest Mr. Highton's device. Multiple transmission did not have moreover its raison d'être, under these conditions, since there was then no time wasted in transmissions.

Rothen translation
"If we look at the pI disc, we find in divisions 2 to 5, 10 to 15, 22 to 25 and 30, in all four notches, in the pII disc 7, in the pIII disc 9, in the pIV disc 10 and in the pV 8 disc, for a total of 38 notches. […] By notching the discs according to the drawing in figure a, we would have obtained 38 jolts for the disc levers, during a single rotation of the latter. The regular functioning of the apparatus would perhaps not have been hampered by these 38 jolts, but, in any case, they would not have been favorable to its functioning, since the levers of the discs are intended to establish the contacts. of the local current of the printer relay. […] M. Schäffler was therefore led to seek a more advantageous solution in the displacement of the notches, so as to obtain a more suitable series of divisions. […] He solved this problem by empire. […] Figure b was formed using 31 small pieces of wood, which could be moved at will. Wood No 1 was set aside, Mr. Schäffler using only 30 permutations. […] He moved the antlers until he came to figure b. This is how we find wood 8 next to wood 21 and so on. This arrangement was the most favorable and the notches of the discs followed each other in such a way that the lever of the disc pI fell once, pII 1 time, pIII 2 times, pIV 4 times and pV 7 times, in all, all the 5 levers 15 times, in a notch, instead of 38 times as in the first arrangement. […] The only purpose of this arrangement is therefore to free Mr. Schäffler's device from a few drawbacks. [...] If now M. Baudot's model resembles M. Schäffler's permutation disks, we can simply conclude that M. Baudot enjoyed the same advantages as M. Schäffler. […] However, the two systems cannot be absolutely equal because Mr. Baudot uses 31 permutations, while Mr. Schäffler is satisfied with 30. […] In general, the two devices are only alike in idea apply the multiplex system to printing devices."

The "notch" I presume is between positive and negative contact regions on the disc, corresponding to bit transitions between codes. Minimizing them is good, and is equivalent to having only one bit transition per code transition. But this guy misses the point. It's not about minimizing the number of jolts but about avoiding the possibility of glitching, when the printing wheel scans for a match to the character code. He got this close to being able to say something about the reflected binary code and it's raison d'être, but flubbed it. I already removed this ref from the article, since it has nothing relevant to Gray code.

More Baudot history
Let's look at how the article's comments on Baudot got to where they are. What we really need are secondary sources that connect these telegraphy bits to Gray codes. I see Knuth does that, so I'm getting a copy to inspect in depth. Dicklyon (talk) 03:01, 24 January 2021 (UTC)
 * In this 2002 edit, we got "The French engineer Émile Baudot used Gray codes in telegraphy in 1878. He received the French Legion of Honor medal for his work.", unsourced, from User:Heron. I presume he got that from a source, but don't know what.
 * In June 2014, at Talk:Gray_code/Archive_1, an IP proposed saying more about Baudot.
 * On July 3, 2014, the IP added a ref to Pickover's Math Book, of 2009, which says "The French engineer Émile Baudot used Gray codes in telegraphy in 1878", quoting our article without attribution. And it has a direct copy, plus color, of the patent drawing that I upload in 2006.  Seems like clear WP:CITOGENESIS to me.
 * On July 4, 2014, User:Glrx pushed back on the talk discussion and asked for a reliable source, but didn't do anything about the article.
 * That's where it sat until December 17, 2020, User:Matthiaspaul started adding a whole bunch of refs about Baudot, most not saying anything in support of him using a Gray code, as far as I can find.

Based on discussion above, and more studying of sources, I've pared it back again. It's clear that both Baudot and Schäffler had discovered and used the essential properties of Gray codes in their printing mechanisms, so it's best to focus on sources that say something about that. Multiplexing and keyboard differences are irrelevant, and assignment of codes to letters nearly so. Dicklyon (talk) 00:40, 25 January 2021 (UTC)


 * I needn't have waited for the Knuth book, as I see I had found it before and linked it above (here). It says "More significantly, Γ5 was used in a telegraph machine demonstrated in 1878 by Émile Baudot, after whom the term 'baud' was later named. At about the same time, a similar but less systematic code for telegraphy was independently devised by Otto Schäffler."  That about it: "used in a telegraph machine" is supported by the sources, but the Gray code is still not very relevant to the Baudot code, or Schäffler's code, itself.  It's an internal detail of the sequential character matching at the print wheel.  Not sure why he says "code for telegraphy" in Schäffler's case.  Dicklyon (talk) 00:07, 3 February 2021 (UTC)

Well-balanced
An IP editor claims the expressions are different from what's given in the ref. ~Kvng (talk) 13:18, 25 May 2021 (UTC)


 * The number of transition in each dimension is necessarily even. The IP's claim look therefore plausible, while the current claim in the Wikipedia article must be wrong. --FvdP (talk) 15:42, 17 December 2021 (UTC)

Lucal code?
I'm not sure why the table of values at the very top of the article also includes a different coding scheme which is not explained anywhere else nor has an article of its own. It makes the table more difficult to read while not adding anything that's related to the article, I suggest it's best removed Ruse.mp (talk) 07:58, 29 December 2022 (UTC)