# Is Morse code a digital, binary mode?

At first glance Morse code looks like a digital mode - there are dits and dahs, two values which contain the information of the transmission. Alternatively, at any point in time there either is a signal, or there isn't.

Morse code follows the following pattern:

• dit: tone for one unit (1)
• dah: tone for three units (111)
• separation between elements: silence for one unit (0)
• separation between letters: silence for three units (000)
• separation between words: silence for seven units (0000000)

As mentioned in a Vsauce video, however, Morse code doesn't actually require only two different values, but actually three: dits, dahs and spaces. He goes on to explain that any Morse transmission can be broken up into three components: a dit with one unit space (10 in his notation), dah with a space (1110) and a separator character (00, two dits in length). From this he argues that it is actually a trinary, rather than a binary code.

But is it?

After all, any transmission can be represented as either a high or low signal voltage at the receiver, sent in a pattern of one bit per dit. The information is encoded entirely in two separate, discrete values. How this information is afterwards decoded is a matter of choice I would argue.

It seems similar to the ASCII scheme - the information to what letter corresponds to what bit sequence is just a matter of definition, but the information is still binary. Analogous to that, Morse code is nothing more than an encoding with variable-length 'bytes'.

From a strict definition (what is it?), is Morse code (CW) a binary mode? Or is it trinary, or something else entirely?

• Asked already here: Is Morse Code binary, ternary or quinary? with extensive answers. – hatchet Oct 29 '18 at 19:26
• I agree, this question has been asked and answered; however, the answers given there are completely incomprehensible to anyone without a degree in computer science. Moreover, I believe the accepted answer is wrong. – Andrew Jennings Oct 30 '18 at 16:13

According to Shannon (in A Mathematical Theory of Communication - and who's going to argue with Shannon?) there are really only four symbols in Morse, not five:

• "dit" (defined as one unit time on followed by one unit time off)
• "dah" (three unit times on followed by one unit time off)
• "letter space" (two unit times off) (should follow a dit or dah symbol)
• "word space" (four unit times off) (should follow a dit or dah symbol)

You don't need a fifth symbol for the intra-letter space because you can't represent a "dit" or a "dah" without some space following it. So by defining the dit and dah symbols as above, you get the intra-letter spaces without adding to the symbol count.

Aside from that, I believe we are dancing around the distinction between line states and the channel code. The line state in Morse usage is binary but the channel code is not. Per Shannon, the channel code has four different symbols.

Another example of a channel code is EFM, eight-to-fourteen modulation, which encodes every eight bits of end-user data as a 14-bit word. The allowable 14-bit words are chosen so that each has zero DC offset (same number of 0's and 1's) and to limit the number of successive 1's and of successive 0's. It is used on Compact Discs and other optical digital media.

• +1 This! Line coding is on/off, but the information cannot be coded as two states. dit-dah alone can mean anything (is it "a" or "et?"). Spaces are necessary to tell characters apart: space-dit-space-dah-space ("et") vs. space-dit-dah-space ("a"). – rexkogitans Oct 30 '18 at 12:54

The mode hams call "CW" is also called "on-off keying" (OOK) - a hint to the fact that it is a binary code. Dots, dashes and spaces are usually sized in multiples of the "dot time": one dot time on for a "dot," one dot time off for the "space" between dots and dashes within a given character, three dot times on for a "dash". Spaces between letters and words comprise other dot time multiples. These multiples can be adjusted for purposes of readability or "personality."

An earlier Ham Stack Exchange answer described how these properties are exploited to improve the signal-to-noise ratio of CW signals.

• Agreed. No matter how you time the dits and dahs, the carrier still only has two possible states: on and off. The separations are simply a component of the information being conveyed. – mrog Oct 29 '18 at 18:23
• "On-off keying" may be a common mode, designated as A1A or A1B, but not the only one for Morse code. When sent as an audio tone modulating an FM carrier, the designation is F2A. This is commonly used for repeater identification on VHF and UHF repeaters, for example. There are many other non OOK methods of sending Morse code. So it would seem necessary to separate the modulation method from the encoding method. Do you agree? – Glenn W9IQ Oct 30 '18 at 13:48
• "So it would seem necessary to separate the modulation method from the encoding method. Do you agree?" ... Yes, I wholeheartedly agree, and made this point in my comment to another post, above. – Brian K1LI Oct 30 '18 at 15:50
• 1110111010101000101010111011100011101010001000 – Cecil - W5DXP Mar 21 at 23:54
• @Cecil-W5DXP Clever! – Brian K1LI Mar 22 at 11:32

I believe the question is confusing the difference between something being a natural basis for a language, versus whether something could be adequately represented by one in a mathematical / encoding sense.

It is clear that morse code can be represented adequately using a binary representation / encoding. This is not surprising, since a binary representation can be created to represent much more complex bases anyway, such as the latin alphabet (e.g. ASCII).

However, you would probably agree that this doesn't make the latin alphabet a binary one in nature. Rather, the alphabet's elementary particles (the letters) can be used to form more complex constructs (the words). So in this sense, the English language is most naturally regarded as a 26-base system (because there are 26 elementary letters-particles).

Similarly, while it is possible to represent morse code using binary encoding, one would be hard pressed to argue that this is the most natural representation for it, or that this makes it a binary 'alphabet'. It is rather intuitive to consider the 'dit', 'dah', and 'separator' as the elementary particles that combine to form more complex constructs ('morse code').

You could of course try to argue that the 'dah' is not a well-suited, natural atomic particle for the morse code language, hence you can accept the 'binary' representation of '10', '1110', '00' etc, but I would argue that this is not really a good interpretation of the nature of morse code words; it is far more intuitive to conceive of morse code letters as composed by elementary dits, dahs, and separators as the elementary particles. If you need three bits to express a 'dah', then you're using essentially using four 'atomic particles' in your chosen representation, to express what is essentially a single natural atomic particle in the morse language, which seems like a rather inefficient way of expressing the language. Remember that binary is the choice of digital signals because of the electrical nature of transistors which deal with such signals most efficiently. But there's no reason for morse code to abide by that requirement, so a more efficient representation which is more natural to morse code (and its transmission by telegraph) would presumably have been preferable to such a binary encoding among telegraphers.

As to the separate question of whether it should be possible to consider the dit and dah itself as a sufficient number of elementary particles to fully express the morse code language, the answer to this is no (and hence it is not a naturally binary 'alphabet'). You can confirm this by attempting to express morse code in the absence of spaces. The reason telegraphers could rely on only dits and dahs is because they also had the added element of time, which could simulate word separation. When these need to be written down on paper as symbols, however, the word separator needs to be made explicit, thus making morse code a ternary system.

Another way to see why time in itself is not a trivial aspect, but actually adds information is to treat it as if it's a separate signal transmitted in parallel with your dits and dahs. You now have two signals to consider at each time point, one in the dit-dah dimension which tells you whether you're dealing with a dit or a dah at that timepoint, and one in the time dimension, which tells you if you're dealing with a dit-dah particle, or not (i.e. a separator). Since these are two independent binary signals, your receiver at the other end would have to process a 4-bit signal. However, this can be encoded more efficiently as a 3-bit signal, since when the time series has a separator, the ditdah series is ignored. Thus the most efficient and natural representation for morse code is a ternary one.

PS. I forgot about the distinction between a 'letter separator' and a 'word separator', but the above arguments still apply. You could make the case for a quaternary base instead of a ternary one incorporating a bespoke 'word separator' particle, or accept the ternary one and accept the inefficiency that comes with always having to represent a 'word separator' using a slightly less efficient representation using a 'diphthong'.

Morse code is sent over a digital link. The link might use electromagnetic waves (in various parts of the spectrum), sound waves, electrical signals in a conductor or any other binary signalling method you can come up with. (E.G. tug on a rope, tapping a pipe or whatever.)

The digital link is modulated between two states, which for CW means turning a carrier wave off and on.

Modern day digital links use a clock signal to break down transmissions into single bit values. Synchronous transmission requires sender and receiver to use a single clock signal which they can both access. Asynchronous transmission means the receiver must reconstitute the timing signal from the received signal.

Samuel Morse did not have to go into these detail. Effectively he used a signal coding scheme of

• On signals of two noticeably different lengths - short and long for dit and dah,

• Combinations of various numbers of dits and dahs to encode letters,

• Off signals of three noticeably different lengths - short to separate dits and dahs, medium to separate successive letters and long to separate words.

The human brain can decode this scheme with training and allow for differences in fists and speed. Mathematical analysis can quantify and assign a number of time units for dits, dahs, and spaces used in standard practice.

While CW might be used in parlance to refer to Morse code it is not the same. CW is a type of digital transmission link. When used to transmit Morse it operates asynchronously - a separate clock signal is not sent.

At a low level, Morse uses 5 ( or 4 depending how you analyse it mathematically) signal state timings to form dits, dahs, inter letter and inter word spaces.

At a higher level Morse interprets dits, dahs and spaces as letter and words.

So Morse code combines multiple sets of coding schemes:

• bit detection: binary, repeating the same bit if it lasts more than one unit of time. More related to computerized decoding rather than by wet-ware in the brain.

• low level decoding: quaternary from the POV that it recovers dits, dahs, inter letter and inter word spaces.

• high level decoding reverses the encoding scheme used to assign dits and dahs to letters and combines them into words. When using "Morse" to refer to the encoding scheme itself, distinctions of binary, ternary, quaternary etc. are out of context.

Fully agreeing with Brian!

From a strict definition (what is it?), is Morse code (CW) a binary mode?

Is Morse code a digital, binary mode?

Digital is easy: A digital signal is a signal

• that only takes discrete values,
• is only defined at a discrete axis (e.g. time, position, angle, impulse…)

The question is: What are the values of your signal, and what's the axis?

I'd not understand Morse as an OOK (though I'd certainly start decoding it as such), but as a "long-short keying". In that understanding, we get as the axis along the signal changes not time, but just "index" (first symbol, second symbol, third…), and as values just "short on", "short off", "long on", "long off", and "very long off".

With that, the dots, dash, inter-dot/dash spacing, inter-letter and inter-word spacing are representable.

So, in that understanding, Morse would be a digital, quinternary code.

• I think I'd recognize six symbols: "short on short off", "short on medium off", "short on very long off", "mediuon short off", "long on medium off", and "long on very long off", which may be assembled in arbitrary combination. – supercat Oct 29 '18 at 20:14
• hm, makes even more sense, @supercat! – Marcus Müller Oct 29 '18 at 20:30

There are two layers to Morse Code.

First: Amplitude Modulation using the two symbols, Mark and Space. This layer is binary. Timing is quantized as the "dit" time. So higher level symbols can be represented as a string of Marks and Spaces aka ones and zeros.

Second: There are four symbols made from the first layer,
dit 10
dah 1110
letter space 00
word space 0000
NOTE: Other combinations of 1 and 0 are not allowed. Disallowed combinations means that there is less information contained in a given number of bits, or alternately, there are extra bits required for a given amount of data (redundancy). This redundancy makes the code more suitable for human recognition.

• Hi Roy, this appears to be an accurate answer however it is confusing in that one needs to really understand the structure of Morse Code before the answer starts to make sense. I am editing for clarity but maybe there are additional details you could consider adding. Thanks! – Chris K8NVH Dec 9 '18 at 13:42

The answer depends on the WPM and the sampling rate. If the WPM is fixed and known, and/or the receiver can phase lock to the the WPM dot transition rate, and you sample the carrier amplitude only once per dot time, you get a binary representation which includes a fair amount of information redundancy (e.g. no tones 2 samples long, etc.)

If you dynamically vary the sampling to once per symbol transition at a fixed WPM, (dot,dash,gap,letter space,word space), then you get a quintic (5 symbol) coding, instead of binary, a little more compact, but less redundant.

If you allow varying the WPM, and sample all the transitions, then you have an additional analog coding on top of the quantized digital coding, as each tone length and gap length can carry information, the amount depending on the rise/fall times, which increase the spectral bandwidth, but still being Morse Code if the short term timing variations stay within some limit (dots don't randomly double in length within some short number of beeps, etc.), and/or the long term WPM speed drift rate isn't too high.

This analog timing channel can carry (encode) quite a bit of information, e.g. you might be able to ID a straight key operator by their "fist", even without their callsign. Or an operator's emotional state by how they vary their straight key keying. This is common in practice (assuming they still make straight keys), and thus might be considered part of Morse Code encoding (in practice, not in the ITU spec.)

I suppose one could even vary the CW envelope rise and fall times to carry even more information over "CW". Although standard HF rigs can't do this, once could do this by using DSP/SDR radios (or SDR audio input to an SSB modulation). Although this might be considered an obscuration code, illegal in some regions unless well documented publicly. This form of "CW" might sound identical to Morse Code, but would really be a different modulation scheme.

It's a matter of interpretation. Consider

-- --- .-. ... . -.-. --- -.. .

As written, it's a trinary code: dash, dot, and space. We can analyze it on a higher level, though: -- represents 'm', --- is 'o', etc. On this level, we have several dozen symbols: you can't translate Morse Code into the normal English alphabet just knowing that - is "dah" and . is "dit", you need to know the whole "alphabet". We can also analyze at a lower level: just as - and . are made up of black and white pixels, dits and dahs are made up of sound and silence, and thus are binary. Certainly, it is false to say "Morse Code is a binary code made up of dits and dahs", in that on that level, it's not binary.

One thing that makes analysis complicated is that Morse Code is that, for many of these levels, we are far from filling the space of combinations. For instance, on the binary level, we have that a dit is 1, and a dah is 11 (or possibly 111), and then there are spaces of 0, 00, 000, or 0000. There is no 0000 or 1111. Going up a level, there are many combinations of dits and dahs that don't represent any character. This suggests that these levels are not the appropriate level to analyze Morse Code.

Of course, any actual physical implementation of Morse Code will not be truly be discrete "silence" versus "fixed level". It's a continuous system, so volume varies continuously between silence and sound, and there's bounce, etc. So there's yet another sense in which communication through Morse Code is done through an analog channel, but interpreted as discrete. The disagreement is then over on what level of abstraction we should consider the conversion from analog to digital to occur. Do we convert each unit of time to a 0 or 1, depending on the volume during that unit of time, and then convert those 0s and 1s to dits and dahs? Do we convert a period of sound surrounded by silence to a dit or dah directly? Or something else?

• Are we conflating "mode" and "code?" Seems to me that binary (on/off) signals are grouped into symbols or code groups to convey information. – Brian K1LI Oct 30 '18 at 3:55
• @BrianK1LI What in my answer are you referring to, and how? – Acccumulation Oct 30 '18 at 4:07

No, it is a ternary system (or trinary system; trinary and ternary are the same).

That's because you only use dots, dashes, and spaces to represent the world. These are called "trits" in a ternary system.

In a binary system, you use only 1 or 0 to represent the world, and these are called "bits".

• I fully agree. The only "space" in a binary system is when the system is powered down. :-) – Mike Waters Oct 30 '18 at 17:27

Interesting question, which really depends on what one means by a "binary" encoding system.

At the lowest level, an International Morse encoded, continuous wave (CW) transmission the signal is either 0 or 1, energy present or not. This is similar to the frequency-shift keying (FSK) encoding used by radioteletype (RTTY) transmission.

• Aside: CW isn't as redundant as FSK, where the encoding is done by shifting the frequency up and down. With RTTY, three states can be determined by the receiver: 0 (space), 1 (mark), or no signal. With CW, the "no signal" condition must be determined by noticing that an excessive time has passed without detection the signal, or a 1.

Both RTTY and CW depend on time-domain decoding to convert the binary sequence into characters.

In RTTY, the time-domain decoding is performed by looking for a space condition (0) and using a fixed timer to sample the signal at specified times. The samples are assembled into a multi-bit character.

In CW, the time-domain decoding is not based on a pre-fixed bit rate. Instead, the receiver watches the binary data flow looking for patterns -- two distinct period durations in which the signal is 1 balanced with periods during which the signal is 0. In a more modern system, we would consider that there is a clock recovery process looking at the 0-1 and 0-1 transition times. Rather than assembling a fixed number of bits, there is a state machine that takes inputs of short-1, long-1, short-0, and long-0, as determined by the clock recovery.

In American Morse, there are two more inputs to the state machine, the extra-long-1 "L"-dash, and the even longer "0"-dash.

So, I suggest that Morse code is a binary encoding system which depends on clock recovery to recover multi-bit symbol information. In this way, it is similar to other digital encoding schemes such as Non-return to Zero Invert (NRZI), and Phase Modulation (PM), as well as more complex schemes such as HDMI, USB, and Ethernet.

Morse code using only a given ratio of lengths is only a binary code because the intelligence is transferred by a two state (on/off) method. Now for the difference, each character is sent via combinations of these on/off signals in various combinations. The old railroad code went even further to change the pulse width, if you will, by changing the spacing distance between pulses, or the length of the dash (short dash / long dash). Normal radiotelegraph code uses a fixed set of binary digits, a dash equal to the length of 3 dots. Therein lies the binary aspect. Just because there is a difference in character spacing which correlates to a baud speed, both are considered binary in nature.

Lastly, if you didn't turn either what we consider a binary signal or a radiotelegraph signal on it wouldn't be binary; if you turned it on and didn't turn it off it also wouldn't be binary.

• Why the caps..? – ahemmetter Oct 30 '18 at 20:20