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How much voltage change, what I'm calling binary data, can be transmitted over a wire at one time in one clock cycle? I understand, I think, binary data is what we call it and the wire doesn't really send out a one or a zero. It is conceptual.

I've been reading the question and have a measure of understanding, but not great. I understand there is a frequency at which voltage is transmitted and represented by us visually/logically as binary data. But how much "data" can be transmitted over a wire in one cycle? Is one cycle one voltage transmission (a bit) across a physical wire? Like Morse code but with computers it ends up being really, really fast (Ghz).

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FYI: Hertz is a measurement of frequency in cycles per second. Meanwhile one cycle can refer to one wave cycle(what audio/radio/light frequencies are based on), or one _clock cycle_(what most data transmissioms are based on). For clarity, I think here what you're wanting to know is "how much data per clock cycle," correct? – Robherc KV5ROB Jan 29 at 21:43
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Data is transmitted in bits per second - that's how folk normally state it so, are you asking how much data can be transmitted in one second? You say "I've been reading the Question" - what question? – Andy aka Jan 29 at 23:04
    
You can transmit no more than log2(1+SNR) bits if your signal bandwidth is only limited by the sample rate. – Steve Cox Jan 30 at 16:43
up vote 13 down vote accepted

Actually, the answer to your seemingly simple question is more complex than you'd readily believe!
The short answer is that one signal at a time can be passed through a single signal wire, in one cycle. The amount of data that symbol represents depends on the protocol used.

The long answer is that:

  • 2-state protocols, like OOK (On-Off Keying), pass only one bit (on or off) per cycle;
  • 1-dimensional multi-state protocols, like FSK(Frequency Shift Keying), PSK(Phase Shift Keying), FM(Frequency Modulation), or AM(Amplitude Modulation), can transfer a few bits of data at once;
  • Multi-dimensional multi-state protocols, like QAM(Quadrature Amplitude Modulation), can transmit fairly huge amounts of data in a single cycle (I've seen QAM 512 {9 bits per cycle} advertised).
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    So how long is a cycle? One second? One billionth? – johnny Jan 29 at 21:44
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    @johnny, the length of a cycle is all down to the frequency of your clock. 1 clock per second (1 Hz) is certainly possible. 1 billion clocks per second (1 GHz) is also possible, but requires a lot more care to design and is likely to cost more. – The Photon Jan 29 at 21:47
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    The length of time for one clock cycle depends on the transmitting/receiving devices. For instance, human operators generally type morse code with cycle speeds between 1/2 and 1/5 of a second, while a 2.5Ghz CPU has a cycle that lasts only 400 trillionths of a second. – Robherc KV5ROB Jan 29 at 21:48
        
    Did you intend to write "...short answer is that one symbol..." instead of "signal"? – guntbert Jan 31 at 20:58
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    @guntbert Yes & No: I meant to convey the idea of one symbol, but chose to use 'signal' instead to avoid confusion as OOK/FM/AM/serial lines don't necessarily use the term symbols AND because I was trying to "Keep it Simple" for the (not-quite-so-technical) level this answer was aimed at. Sometimes, being slightly less precisely correct is better than being exactly right, but causing confusion for your audience & miss conveying the point entirely. – Robherc KV5ROB Jan 31 at 22:04

    Welcome to SE, Johnny. You have a few terms mixed up. I take it from the question you want a beginner's grasp of what's going on.

    Hertz is the number of cycles per second.

    A very simple explanation

    A (simplistic) way to understand this would be to imagine a signalling system that transmits ones and zeros as pulses.

    schematic

    simulate this circuit – Schematic created using CircuitLab

    Figure 1. Transmission of code '1 1 0 1 0' using pulse-width modulation.

    Encoding the data

    In our simple transmission system a '1' is transmitted using a long pulse. A zero is transmitted using a short pulse. In Figure 1 we show how to encode the signal using pulse-width-modulation and transmit a binary signal.

    Data speed

    • If we transmit one pulse per second we will have a 1 Hz signal (one cycle/second) and we will transmit one 'bit' (binary digit) per second.
    • If we increase the transmission speed we can transmit move bits per second.

    For such a simple system you can think of the data speed as being the same as the pulse rate. So to transmit 9,600 bits per second you would have 9,600 Hz.

    Limits on data speed

    So why don't we transmit everything at high speed? There are several reasons but one of the easiest to appreciate is that cable has capacitance and inductance. The effect of these is to mess up the nice square wave we have generated and instead of a nice square-wave what comes out the other end is more of a triangular wave. As we keep increasing the frequency the signal gets worse and worse until we can't read it reliably.

    There are various methods used to maximise transmission speed and reliability and, as the other answers have indicated, it gets highly technical pretty quickly. The simple general rule is that the longer the cable or transmission distance the more degraded the signal becomes and so lower data rates have to be used.

    Please clarify your question if I've pitched this answer to high or too low.

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    You forgot to mention noise... Noise is the real reason we can't send billions of bits as fast as we want. There are detection limits. Comm theory – laptop2d Jan 29 at 22:21
        
    I think that would have added 'noise' to my answer (which is deliberately very basic) and transmission of the central idea might have been lost. 8-) Let's see what the OP wants. Thanks for the comment. – transistor Jan 29 at 22:27
        
    This answer discusses only one protocol (pulse width modulation) out of the many available. Bit rate would be a better word than frequency (9600baud instead of 9600Hz.) The actual bandwidth to get a well formed signal with reasonably sharp transitions will be at least 5 times the bitrate. There are also binary modulations of radio frequency carriers, which are a very different protocol discussed in Robherc's answer. – Level River St Jan 29 at 23:42
        
    Again, OP appeared to be confused about hertz and I didn't want to get into bits-per-baud, bandwith, encoding schemes, etc. I thought I made this very clear in my answer. OP has accepted Robherc's answer so it appears that I aimed too low. – transistor Jan 29 at 23:48

    As laptop2d and transistor say, NOISE! That's the key concept. Everything else is just signal (sorry, I couldn't resist that).

    Back up a minute and simplify the question. Consider just an unchanging voltage on the wire, supplied at one point and measured at another. And let's say that the transmitting (supply) end is a theoretical textbook-perfect power supply. The transmitter drives a certain voltage on the wire. At the receiving (measuring) end, we ask the question, "What is the voltage?" If all we can say is, "Eh, about 1.2V.", that's not a lot of information. If we can truthfully say, "It is 1.23798570520664V, give or take a few femtovolts", then that is a lot more information. In fact, if there was no limit to the precision with which we could supply and measure a voltage (and nothing interfering with it along the way), there would be no limit to how much information we could stuff down a wire.

    In the real world, our precision is limited because of noise. There is noise in any real voltage source, noise due to thermal excitation of the wire, noise in the measuring instrument, and so on. There are also other practical limitations because of real-world tolerances on component values, reference sources, and more, but we don't even need to think about those to see that we can't supply and measure a voltage with unlimited accuracy.

    So, how do we get more bits down a wire? We trade off accuracy and time. For example, instead of trying to measure a voltage once at femtovolt accuracy, we split the data up and make multiple measurements at, say, millivolt accuracy, spread apart over some period in time. Now things start to get really interesting, because there are so many different ways you can do this, and the reason there are so many different schemes in use is because they each make a different set of tradeoffs with regard to speed, complexity, cost, power, robustness, and what have you. Also, as others have mentioned, once you throw the time element into it, you have a new set of problems in addition to pure noise, because there are distortions and reflections that limit how quickly you can make changes at the source and get a distinct result at the receiver.

    So, to get back to the original question, "How much binary data is transmitted across a physical wire in one Hertz cycle?", it all depends on how you transmit and receive it. If you want to dig deeper, the field is called "Communications Theory", and Claude Shannon is its patron saint.

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    If the data is being transmitted synchronously with a clock shared by the transmitter and receiver, then the number of meaningful voltage changes (0 to 1 and 1 to zero. between clocks) will depend, to a first approximation, on the characteristics of the transmission medium and the impedance of the load.

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