What are "Bits" and "Bytes", and why do you care?

Scott Borduin

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Honestly, I'm not entirely sure why you might care, but I'll do my best to make the read worthwhile :)

It is pretty much impossible to navigate the modern world without, at some point, being exposed to the fundamental computing concepts of Bits and Bytes. Sometimes these words are used metaphorically, as a way of saying "down in the details" - for instance, "I'm not interested in the Bits and Bytes". In other cases, they are used in a general technical sense, for example: digital audio bitstream, 10 Bit video, 24 Bit audio recording, 64 Bit processor, 100 GigaByte disk. And there are other words directly related to the concept of Bits: "Ones and Zeros", "Binary", "Digital". We use those concepts and words all the time, but what do they really mean?

A "Bit", in computing, represents the smallest unit of information that can be represented - the smallest bit of information, get it? Bits are to computing what protons, neutrons, and electrons are to physical matter, the basic building blocks from which all, more complex structures are created. Just like the atomic particles can be used to "build" everything from Hydrogen to Mount Everest, Bits have an essentially infinite capacity to represent the different kinds of information, aka "data", in the computing universe.

And what is a Bit, exactly? Well, it is a piece of data with exactly two possible values (aka "states"). These values are often referred to as "zero" and "one", or "off" and "on". The "off" and "on" wording gives you a major clue as to why the Bit was chosen as the fundamental unit of data for computing. An electrical switch has two possible values: off and on. And computers are mostly, in the most reductionist sense, collections of electrical switches. Millions of them. That's what a "chip" is - a collection of interconnected electrical switches.

If you walk over to the nearest light switch right now and flip it on or off, you are setting the value of one "Bit" of information. How do you know what the value is? Well, either zero volts comes out of the switch, or about 120 volts comes out (assuming you're in North America). So 0 volts = Off, 120 volts = On. The light bulb is the "detector" that tells us which is which. In a modern computer, the switches are implemented as microscopic transistors, and they mostly transmit voltages to other switches rather than light bulbs, but the fundamental concept is largely the same.

You may wonder about the above analogy. What if we have a dimmer switch, instead? Then the voltage can vary anywhere between 0 and 120 volts. And we could, say, arbitrarily scale that range into steps of 10 volts, and our switch could then represent 12 different values instead of two. Or we could divide it up even more finely. Wouldn't that be a more efficient use of a single switch? Yes, indeed, it would, and there is a quite different concept of computing called "analog computing" which essentially does exactly that. The problem with analog computing is that it is too dependent on uncontrollable factors in the computing environment. To use the dimmer switch analogy: what if your air conditioner switches on and briefly drops your voltage to 100 volts? Oops, your scale is now off and your data is corrupt. What happens when the dimmer wears, and doesn't put out the same voltage for a given switch position as when it was new? What happens when we have to transmit our dimmer signal halfway around the world on the internet - how good will our scale work then? Now multiply that uncertainty by hundreds, thousands, millions of switches - it's not going to work.

The powerful thing about "binary data" representation - ones and zeros, on and off - is that it greatly increases the margin of error when interpreting our data. In the case of our light switch, 0 volts or 1 volt or 2 volts are all trivially interpreted as "off", and 80 volts or 140 volts or whatever is still trivially interpreted as "on". Binary data representation, in a favorite word of computer scientists, is highly "robust" - highly immune to the kinds of variations present in all real world systems.

OK, so now we've established why a Bit is a piece of data with exactly two possible values. Still, what the heck are we going to do with that? We're going to make numbers out of it, that's what. Observe this number: 111. How many objects does that number represent? One hundred and eleven, of course. Of course? Let's break it down a bit, going back to that grade school math. Remembering our addition and subtraction rules, we know that the number 111 has a 1 in the "ones" column, 1 in the "tens" column, and 1 in the "hundreds" column. 1 times 1 plus 1 times 10 plus 1 times 100 is one hundred eleven. We use the same rule for 999, or other combinations of three digits. By using those ten possible digit values in each column, combined with those simple rules, we can represent any number.

The computer doesn't play by those rules. It mocks our choice of ten possible values for each digit as an arbitrary rule originating in the unimaginative observation that the median human has ten fingers. So easy to lose track of how many fingers you've used, and how many times. Here's how the computer interprets 111: 1 times 1 plus 1 times 2 plus 1 times 4. In english, seven. Each "column" in the number is a multiple of 2 over the previous column, rather than a multiple of ten. By simply using a different rule, called a "base-2" or "binary" number system, rather than our "base-10" system, the computer can use a sequence of bits to represent any number. Using 8 bits, the computer can represent numbers from 0-255, using 16 bits, 0-65535, and on. The bigger the number you want to represent, the more bits you need, but there is no theoretical limit on how many bits you can use.

It may not be so obvious, but once you've got numbers, you've got pretty much everything you need to represent any kind of data you might want. Text, for instance. Computers have to do lots and lots of processing with text. Fortunately, text in any language can be described with a finite number of symbols; all you need to do is assign each character or punctuation mark or other symbol a number. IBM computer scientists observed that the range of numbers 0-255 - eight bits - was enough to assign a number to each symbol used in common English text, and defined a table of number-to-character correspondence called EBCDIC. In EBCDIC, for instance, "a" is assigned the number 129. Today, in a global internet-connected world, language symbols are usually represented by 16 bit numbers, due to the greatly larger number of symbols needed for languages like Chinese and Japanese. But for a long time, given the Western origins of modern computers, and the limited memory available in early computers, eight bits for a text character was standard. So standard, in fact, that eight bits got its own shorthand name: "Byte".

So a Byte is just eight bits, and represents the smallest unit of information that is actually useful to a computer user, rather than the computer itself. As such, the Byte became the unit of measure for memory and storage in a computer. A kilobyte is 1000 bytes, megabyte is a million bytes, gigabyte is a billion bytes. To give you a feeling for how far we've come, a typical Mac or IBM PC in the early 80s would have 32 or 64 kilobytes of memory. A "starter" laptop today usually has 2 gigabytes of memory - more than 30,000 times as much!

There are many other creative ways that numbers can be used to represent data - audio, video, pictures, and other physical and virtual realities. We don't have space in this already long post to go into all of them - we'll get to some later. But I want to end by addressing a philosophical objection which often arises in discussions of using numbers or digits or bits to represent aspects of the "real world". This objection is, of course, well known to audiophiles. Roughly stated, the objection is that "chopping up" reality into bits is inherently a flawed, imprecise process and therefore inferior to older, analog-style representations of reality. If we hear a digital recording and hear things we don't like compared to analog recordings, or see a digital photograph and see things we don't like compared to film, we might naively attribute those things to the "discontinuous" nature of digital representation compared to the "continuous" representation of the older analog medium. The truth is, reality itself is discontinuous, and so are any representations of it. Analog audio recordings are captured as bits of magnetic media, and vinyl records are composed of very large (by atomic standards) chains of molecules. Pictures and film are composed of small particles of pigmented chemicals. And so on. There is nothing "unnatural" about breaking down reality into bits; in fact, it is the foundation of that magnificent computer we call the Universe.

To put the final meta stamp on this post, I leave you with a digital visual representation of an analog vinyl record.

record_groove..jpg
 
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vinylphilemag

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So a Byte is just eight bits, and represents the smallest unit of information that is actually useful to a computer user, rather than the computer itself. As such, the Byte became the unit of measure for memory and storage in a computer. A kilobyte is 1000 bytes, megabyte is a million bytes, gigabyte is a billion bytes.

Thanks for the great post--but the CS guy in me wants to take issue with that statement. A kilobyte is 2^10 bytes (i.e., 1024 bytes); similarly, a megabyte is 1,048,576 (1024^2 or 2^20) bytes, and a gigabyte is 1,073,741,824 (1024^3 or 2^30 bytes). In marketing-speak (especially when it comes to disc capacities), the base ten system you use is prevalent (although IMHO, wrong: I don't buy in to the KiB, MiB, and GiB units...

To put the final meta stamp on this post, I leave you with a digital visual representation of an analog vinyl record.

View attachment 1574

Nice pic!
 

Scott Borduin

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Jan 22, 2011
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Thanks for the great post--but the CS guy in me wants to take issue with that statement. A kilobyte is 2^10 bytes (i.e., 1024 bytes); similarly, a megabyte is 1,048,576 (1024^2 or 2^20) bytes, and a gigabyte is 1,073,741,824 (1024^3 or 2^30 bytes). In marketing-speak (especially when it comes to disc capacities), the base ten system you use is prevalent (although IMHO, wrong: I don't buy in to the KiB, MiB, and GiB units...

Busted! I've gotten lazy with those concepts through the years ...
 

amirm

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Thanks for the great post--but the CS guy in me wants to take issue with that statement. A kilobyte is 2^10 bytes (i.e., 1024 bytes); similarly, a megabyte is 1,048,576 (1024^2 or 2^20) bytes, and a gigabyte is 1,073,741,824 (1024^3 or 2^30 bytes). In marketing-speak (especially when it comes to disc capacities), the base ten system you use is prevalent (although IMHO, wrong: I don't buy in to the KiB, MiB, and GiB units...
Sadly, this has gone beyond marketing and become the "standard." Anytime one is talking about data storage and communication rates, the units are 1000. In other cases, are 1024. So in that sense, Scott was half right.

And while we are being anal :D, "disc" means optical storage. Disk means hard disk storage. Both are measured in units of 1000.

And to make the topic complete, if you are talking about bits, use the little "b" and when we are talking Bytes, use the big "B." Even tech magazines routinely use the wrong notation and even interchange bits for bytes! To be abundantly clear, I try to spell out Bits and Bytes. So I would say 10 KBytes instead of KB.
 

garylkoh

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Even more sadly, the marketing-types can't even be consistent. I buy two hard drives (different brands) that are both marketed as 120GB, get them home and pop them into a computer and one reads 111Gb and the other 119GB.
 

microstrip

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Scott,

You did an excellent job discussing bits and bytes, but I would like to add a few comments.

Analog computers process analog voltages and perform mathematical operations such as addition, multiplication, integration and differentiation using electronic circuits – usually done with operational amplifiers, capacitors and resistors. The input and output signals are considered as analog variables and can vary in a continuous way – they have no relation with digital. Your twelve position dimmer would represent a twelve state digital signal – and a digital computer could be built to handle these digits, but it would be really complicated! Some experimental non binary computers were built in past.

As you say the reason why computers use a binary system is because implementing such a system in electronics is robust and cheap, but also allows very fast operations. Computers are less clever than humans (e.g. they only know how to add 0’s and 1’s and we know all the tables between 0 and 9) , but they perform much faster and this gives them their power. Also, grouping large numbers of bits you can represent large amounts of data that can be processed very fast.

Where we must disagree is in your sentences about “the philosophical objection”. The existing objection is not philosophical, it is physical and it exists. At macroscopic level the real for humans the world is continuous or analog (although there is a well known exception - the retina, that can precept bursts of photons).

Only at the submicroscopic dimensions (atomic and subatomic) matter is ruled by quantum physics, where you have discrete values - but you are still very far from the values needed to describe the physics of sound reproduction. Your description of “Analog audio recordings are captured as bits of magnetic media” is misleading. Mixing is the same bag analog noise limitations and digital truncation is a poor argumentation against the naïve argument that you want to dismiss, that digital is not natural.

The argument about image grain just shows that there are resolution limits in the chemical photographic process, but does not add any value to your argument. I still do not understand the meta stamp – is it a pro or against argument? :)

The real audiophile objection is not philosophical – it is experienced and very complex. I am sure that it is technological and it why I have interest in WTB debates. We have plenty of experienced people in analog and digital audio around, and, although I do not think we will be able to solve the “audiophile analog-digital dilemma” we can have some entertaining and enlightening debates.

Perhaps I am being too nitpicking, but I think only this way we can understand the problem.
 

fas42

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I am sure that it is technological and it why I have interest in WTB debates. We have plenty of experienced people in analog and digital audio around, and, although I do not think we will be able to solve the “audiophile analog-digital dilemma”

Good to see you here! Yes, the answer is "techological", people are just not trying hard enough yet. The dilemma will be solved when enough people pull their fingers out and actually really try to understand what's going on. In video this "problem" was brushed aside very quickly, no-one(?) complains about digital images not being real or convincing, it was a simple case of getting enough resolution and the circuitry to work properly. The same is relevant to audio -- it's just that the ear is much more sensitive than the eye, of the order of a thousand times more, so you have to work harder to fool the ear.

Sooner or later people will "get" it, it's only a matter of some energy being put into it, by people with the right attitude ...

Frank
 

Scott Borduin

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Jan 22, 2011
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Scott,

Where we must disagree is in your sentences about “the philosophical objection”. The existing objection is not philosophical, it is physical and it exists. At macroscopic level the real for humans the world is continuous or analog (although there is a well known exception - the retina, that can precept bursts of photons).

Well, we tend to perceive the world as continuous, but in fact it is discontinuous at scales far larger than the atomic level. There is no such thing as a "smooth" surface, for instance - all physical surfaces are jagged at sufficient levels of magnification, regardless of what our eyes or fingers tell us. If the point you are trying to make is that humans cannot distinguish discontinuity below a certain threshold, that our senses have finite resolution, well of course that is true and I agree.


Only at the submicroscopic dimensions (atomic and subatomic) matter is ruled by quantum physics, where you have discrete values - but you are still very far from the values needed to describe the physics of sound reproduction. Your description of “Analog audio recordings are captured as bits of magnetic media” is misleading. Mixing is the same bag analog noise limitations and digital truncation is a poor argumentation against the naïve argument that you want to dismiss, that digital is not natural.

I think my argument is not complete, but it is not misleading. An analog tape recording does indeed attempt to represent the voltage of an electrical signal with particles of magnetic material, and the resolution floor and noise characteristics of analog tape are very much related to the finite, discreet nature of the medium at a microscopic level (just as in the film example). In digital recording, the resolution and noise floor are also very much related to the finite, discreet nature of the representation. Both mechanisms are discontinuous at a certain level, and the consequences of those discontinuities are readily predicted and measured - and heard, under the right conditions.

Both digital and analog have theoretically arbitrary resolution, but both are limited in practical implementations. Which is "better" is a whole different story, which brings us to ...

The real audiophile objection is not philosophical – it is experienced and very complex. I am sure that it is technological and it why I have interest in WTB debates. We have plenty of experienced people in analog and digital audio around, and, although I do not think we will be able to solve the “audiophile analog-digital dilemma” we can have some entertaining and enlightening debates.

I agree. For the most part, the objection is not philosophical, although I certainly hear the "chopped to bits" argument still from time to time. The argument is instead, I believe, about two different notions of what "accuracy" is.

When audiophiles like us talk about sound that is "accurate" or "real", we are in fact not talking about absolute fidelity to the original, which is not even remotely achievable in an absolute sense - that is, if we define the original as the soundfield produced by live instruments in a performing space. Two loudspeakers (or 3 or 5 or 7) in a domestic listening space, playing back an audio recording, will create a soundfield that is very different from that heard live in the original space, in ways that are measurably and audibly quite significant. The end-to-end recording and reproduction chain introduces major errors relative to the live performance reference, and there is nothing we can do about that.

But we don't really care, because what we really mean by "accurate" is the recreation of the objective and subjective impressions we remember from live musical performance. We are looking for a good illusion. And the things which create a good illusion sometimes correspond to things which are technically accurate - and sometimes they don't. For instance, the three microphone recording technique used by the early RCA and Mercury recordings, and subsequently by Telarc, creates large amplitude and phase errors in the recording. But the exaggeration of amplitude difference, and the random phase distortion, are perceived as pleasing and suggestive of reality, because they help compensate for the limitations of stereo and room. There are many other examples of such compensatory distortions.

This is one area where objectivist/subjectivist arguments so often run aground. The objectivist position is that everything ought to be as technically accurate as possible. It is often implied that those who prefer inaccurate components are deluding themselves, because of their technical illiteracy. The subjectivist position is that what sounds accurate is accurate. It is often implied that if it sounds better, and the measurements don't agree, the measurements must be wrong or irrelevant. The mutual lack of empathy and respect is often startling, and certainly unproductive. It does objectivists no good to ignore the observations of experienced listeners about what sounds good, and it does subjectivists no good to reject the idea of objective underpinnings to their preferences.

Circling back to the analog/digital thing: as I said, in theory both technologies are theoretically capable of almost arbitrarily good technical accuracy. In practice, if you feed the electrical representation of a music signal through state of the art analog and digital recording/playback gear, the errors introduced by the analog recording/playback will be much larger in magnitude than the errors in the digital recording/playback. That is simply a fact, documented ad infinitum. The errors are not identical in character, but comparing the signal coming out vs. the signal coming in, the digital gear changes it less. Measuring instruments are very good at detecting small errors, and the errors introduced by recording/playback gear are, for the most part, plenty large enough to be measured.

But measuring instruments are not human beings, and can only tell us so much about how errors will be perceived. For instance, the pre-ringing distortion of certain types of digital anti-alias filter in a 44.1K recording is thought by many high-end digital designers to be audibly consequential in small doses these days (see Meridian, Ayre, et al). And some of the kinds of background noise, frequency response errors, and reduced channel separation of analog LPs - although quite large technical errors by the standards of digital - may often be perceived as beneficial rather than detractive.

In the end, nobody is under the slightest obligation to prove in any technical sense that their preferences are valid. Listening to music is about enjoyment, not numbers and facts and measurements and arcane theory. At the same time, a technical understanding of what we like and why, and equally important, why not, is ultimately necessary to move our hobby forward.
 

fas42

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we are in fact not talking about absolute fidelity to the original, which is not even remotely achievable in an absolute sense - that is, if we define the original as the soundfield produced by live instruments in a performing space.
Sorry, profoundly disagree. This is something that seemingly only a small number of people have experienced, that you can recreate a soundfield which is extremely convincing, from only two speakers. There is a huge divide between the one or two who know what's possible, and everyone else, which is what makes it so hard to get the concept across. Once you've been there ...

Again, the technology can do it, it's just that it has to be finely tweaked, and that seems to be the stumbling block: people are totally unwilling to go the extra yards to make it happen.

Frank
 

Scott Borduin

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Sorry, profoundly disagree. This is something that seemingly only a small number of people have experienced, that you can recreate a soundfield which is extremely convincing, from only two speakers.

You are partly missing my point, and partly amplifying it :) I use "soundfield" in the acoustical engineering sense, representing the totality of the sound reaching the listener in a given situation. The soundfield in a small room, from two speakers, in the quasi-near field, will be very different from the soundfield in a large space, from a variety of sources, in the predominantly reverberant field. The directions, intensities, and decay times of the sound will be different, there will be early reflections, there will be aural crosstalk, and all of that is before you get to the inevitable frequency response and phase errors introduced by microphones, speakers, and room. There is no way to create an accurate physical replica of a live soundfield using audio equipment, and that is a simple physical reality.

But as I tried to point out above, creating a convincing illusion is quite a different thing than creating a technically accurate replica. And convincing illusions are their own justification. If that weren't true, I'd listen to AM radio instead of Berkeley, Spectral, and Magico.
 

amirm

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Little confused how this latest discussion relates to bits and bytes! Hope the conversation converges to that :).
 

Scott Borduin

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Little confused how this latest discussion relates to bits and bytes! Hope the conversation converges to that :).

LOL. Point taken. I probably shouldn't have baited the subject in thread starter post, although it's hard to figure out how to make some of these subjects interesting without involving topics people are invested in.
 

microstrip

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I think my argument is not complete, but it is not misleading. An analog tape recording does indeed attempt to represent the voltage of an electrical signal with particles of magnetic material, and the resolution floor and noise characteristics of analog tape are very much related to the finite, discreet nature of the medium at a microscopic level (just as in the film example). In digital recording, the resolution and noise floor are also very much related to the finite, discreet nature of the representation. Both mechanisms are discontinuous at a certain level, and the consequences of those discontinuities are readily predicted and measured - and heard, under the right conditions.

There is a point in your argument that I must rebut for the proper understanding of the problem - resolution and noise floor are very different in analogue and digital systems, although people often mix them. Analogue has per si infinite resolution, but its resolution is limited in practical terms by noise, that is random process. In digital systems resolution is limited by the number of bits, that is deterministic and subject to systematic (non random) errors, but noise is dominated by the analogue noise of the implementation, or the mathematical process of making the conversion.

The relative importance of these contributions will depend mainly on the technical details of the implementations . The physics of the referred processes in analog and digital are really very different and separate the analog and digital representations.

BTW, it was a pleasure to read that we share the same global ideas about sound reproduction.
 

fas42

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Sorry, Scott, about my misunderstanding the intent of your point. Of course, it is a nonsense that that the soundfield in a venue is relevant to the hearing experience, because it varies at every point within the venue. Put a thousand different microphones at different seats in the auditorium, you'll get a thousand different recordings. Yet were I to listen to that performance moving to each one of thousand different seats while the music was being performed, I would still be certain that I was listening to the same event, the quality of it would not vary as an experience. In other words, the technically accurate replica is a nonsense because no such animal exists as an absolute, and not relevant, because the ear/brain does the work of assimilating what's required to perceive the event, and rejects that which is not important.

The key argument is then whether the bit and bytes have enough information encoded in them which can be projected into a listening room by two speakers, with the noise level, both in the classic sense and that which represents distortion, at a sufficiently low level that the ear/brain can still digest the information within sufficiently well for a totally convincing illusion to be experienced.

Frank
 

fas42

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Sorry, last OT bit :), a thought experiment. I'm sure it's been done before, I would welcome if people can point to some info.

A concert hall, with orchestra playing. At some place in the seating area, a small, completely soundproof structure is constructed the size of a living room, and with internal walling to match and furnished accordingly. On the side facing the stage two windows are cut out, nicely rounded edges if you wish, the size and height, elevation and width between them matching a decent stereo speaker setup.

Would the listeners inside hear rough and ready sound that didn't convince as being real? Would it sound like a typical high end system? Would it sound distorted, out of whack? Would they say, this is obviously only a reproduction of something, not like an actual event? Curious ...:)

Frank
 

amirm

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Frank, I am going to ask that we move general audio debates to other threads. Please. This thread is about bits and bytes and computer software in general.
 

fas42

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Sorry, I knew I was being naughty! :). The on thread concept I was pursuing, or attempting to, was that bits and bytes are the essence of what's necessary for communicating information, whether it's a program, raw business data or a musical event capture. A little bit of Shannon, shall we say ...

Frank
 

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