Talk:Gray code

}

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)

@Matthiaspaul: 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)

@Matthiaspaul: 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

Rothen, Timotheus (1878-12-25). "La télégraphie et quelques autres applications de l'électricité à l'Exposition universelle de 1878: Appareils duplex, quadruplex et multiplex". Journal Télégraphique. La télégraphie et quelques autres applications de l'électricité à l'Exposition universelle de 1878 (in French). IV / #10 (12). Berne, Switzerland: Le Bureau International des Administrations Télégraphiques: 247–254 [252–254]. eISSN 2725-738X. ISSN 2223-1420. ark:/12148/bpt6k5661719x. Archived from the original on 2020-12-19. Retrieved 2020-12-19.

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.

• 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#Baudot code, one of the first use of Gray code, 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.

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)

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)