Legal Metrology, Metrication and Bytes

Introduction

The history of measurement dates back millennia, but today's legal metrology and metrication first came into being in France in the late 18th century to address a state of chaos in international and domestic trade and commerce due to the lack of standard and easy to understand units of measure. At the time France alone is estimated to have had 250,000 different regional weights and measures in use (Alder, 2002). However, it was the time of the French Revolution so the new French republic was well situated to attempt radical reform. In the 21st century it is time that we applied the same logic to bits and bytes (in this article I will simply refer to bytes as shorthand for both, though I am aware they are not the same thing).

Several articles have been written regarding the confusing state of affairs concerning bytes, with most noting the relatively recent development of international standards (IEC60027-2 which is  now superseded by ISO/IEC 80000, plus IEEE 1541-2002) supposedly designed to clarify the situation regarding "decimal bytes" and "binary bytes" (although so far this IEC standard has only been formally adopted by the European Union). I will review the findings of some of the more significant articles on this topic, and highlight some of the issues caused by the promotion of a dual standard for bytes.

I will argue that whilst the new international standards are a welcome development they fail to address the underlying issue that bytes are not a legal unit of measure. As will be explained, this is largely due to the fact that the foundation of modern legal metrology - the SI Units - do not technically apply to bytes as (even more technicalities here) bytes are a count and not a measure at all. This is despite the fact that the new international standards allow for the use of "decimal bytes" and "binary bytes", because the inappropriate use of SI Unit Prefixes for "decimal bytes" is regarded as merely common usage of these SI Unit prefixes. In other words, SI Unit prefixes have been unofficially hijacked for use with "decimal bytes", which means that not even "decimal bytes" are a legal unit of measure. True, "decimal bytes" are at least metric, but they are not an SI Base Unit and nor are they an SI Derived Unit.

Whilst the clarification of standards for bytes is a logical and necessary precursor to giving bytes legal status as a unit of measure, they are insufficient in themselves to establish bytes as a legal unit of measure and even go so far to explicitly exclude bytes from SI Unit Prefixes. I will argue that the international organisations who are responsible for legal metrology and metrication have failed in their duties by abdicating responsibility for promoting bytes as legal units of measure (or some alternative legal unit).

Taking Australia as my example, I will conclude by arguing that the ubiquitous reliance on computers in science, defence, industry, education, business, our homes, our transport and in our hands every day demands that we ought to insist upon new laws to ensure that all nations adopt the new standards for "decimal bytes" and "binary bytes". These new standards must then be strengthened by the formal inclusion of bytes as legal units of count by extending the existing international framework of legal metrology - the SI Units - to bytes.

SI Units

Before proceeding further, it is worth noting that there are only seven SI Base Units defined by the International Bureau of Weights and Measures (BIPM) in their SI Brochure (8th ed.):

All other standard units approved by the BIPM can be derived from these seven base units - hence the term SI Derived Units (e.g. area, speed etc). Hertz is a term used in computing (for measuring the clock speed of the central processor unit) that is also an SI Derived Unit.

SI Unit Prefixes apply to both SI Base Units and SI Derived Units. In addition, there are a number of non-SI units accepted for use with SI. Bytes, however, are not SI Base Units, nor SI Derived Units and nor are they considered to be a non-SI Unit accepted by BIPM for use with SI Unit Prefixes. A margin note for SI Unit Prefixes attempts to explain the BIPM position (BIPM, SI brochure, Section 3.1):

"These SI prefixes refer strictly to powers of 10. They should not be used to indicate powers of 2 (for example, one kilobit represents 1000 bits and not 1024 bits). The IEC has adopted prefixes for binary powers in the international standard IEC 60027-2: 2005, third edition, Letter symbols to be used in electrical technology - Part 2: Telecommunications and electronics. The names and symbols for the prefixes corresponding to 2¹⁰, 2²⁰, 2³⁰, 2⁴⁰, 2⁵⁰, and 2⁶⁰ are, respectively: kibi, Ki; mebi, Mi; gibi, Gi; tebi, Ti; pebi, Pi; and exbi, Ei. Thus, for example, one kibibyte would be written: 1 KiB = 2¹⁰ B = 1024 B, where B denotes a byte. Although these prefixes are not part of the SI, they should be used in the field of information technology to avoid the incorrect usage of the SI prefixes."

Note that BIPM seems to infer that SI Unit prefixes apply to bits and bytes with its example of a kilobit being 1,000 bits. Also note that the (original) hyperlink in this quote is to an article by the National Institute Of Standards and Technology (NIST) in the USA. The NIST article repeats the BIPM inference by comparing examples of binary and decimal definitions. In both cases this is misleading, as bits and bytes are not actually part of the SI Units at all.

The USA is one of only three nations that has not yet formally enshrined the use of SI Units in law. Hence although SI units are gradually increasing in popularity in the USA, the most commonly used measurement system in the USA is its version of the imperial system which is known as United States customary units.

The BIPM position on decimal bytes is ambiguous here. Does "incorrect usage" just mean the use of SI Unit Prefixes for binary bytes, or does BIPM mean that any usage of SI Unit Prefixes for bytes is incorrect (given that bytes are not listed as a SI Unit in the SI Brochure)? However, BIPM clearly explain that SI prefixes "refer strictly to powers of 10" which can easily be done for decimal bytes.

Also note the repeated use of the word should here. Should is not must - for must you need legal metrology.

Importance of Metrology

Imagine going to your local grocer and asking for a Kilogram of apples. This week you also ask for a Kilogram of bananas, and discover when you get home that the bananas weigh more than the apples. It turns out that the Kilogram used by your grocer varies depending upon the product you buy! Outraged, next week you decide to switch grocers. You make absolutely sure that a Kilogram is the same for both the apples and bananas. However, you get even less for your money for both apples and bananas. Your new grocer defines a Kilogram differently to your old grocer! You try a third grocer, only to discover that he doesn't use Kilograms at all!

This fictional example illustrates the world we lived in before modern-day legal metrology came into existence. Every now and then we still get a very public glimpse of this archaic and chaotic world. Take for example the loss of the Mars Climate Orbiter, a multi-million dollar robotic space probe that crashed into Mars due to a mix up between the metric system and the imperial system of measurement.

Usually however we barely notice our dependence upon legal metrology. Yet legal metrology is a multi-billion dollar industry. In Australia the National Measurement Institute (NMI) estimates that in a developed country legal metrology has an "added value" of between 3 and 6 percent of GDP. Even at the lower estimate of 3 percent, as the NMI points out, that's AUD $15 billion in Australia alone (NMI, 2009).

Trade, technology, science, sport, food, medicine - legal metrology underpins all these and more, and the SI Units underpin all legal metrology. The only comparable industry in terms of its widespread yet often invisible and deeply significant influence is information technology which underpins every industry and has revolutionised industries such as telecommunications, photography, and entertainment (especially television / film, video games and music) in just last decade. The advent of the internet alone has transformed our world, ushering in a new information revolution that surpasses the one caused by invention of the printing press. With the growth of the internet projected to quintuple between 2008 and 2012 (CISCO, 2008) the revolution is a long way from over.

The Joint Declaration of the BIPM, OIML and ILAC on the importance of legal metrology to trade also emphasises the essential need to trace legal metrology back to the SI Units, which excludes bits and bytes. Bytes underpin information technology, yet in regards to bytes we live in the dark days before legal metrology.

Decimal and Binary Gigabytes - Exponential Confusion

It is worth briefly reviewing the issues related to terminology for bytes, so let's consider the commonly used term Gigabyte as an example. It might seem reasonable to believe that, with just two possible standards (for binary and decimal bytes) there can only be two possible values for the number of bytes in a Gigabyte - either 1,000,000,000 bytes (one billion bytes) or 1,073,741,824 bytes. However, this is not the case.

A Megabyte is sometimes expressed in terms of the number of Kilobytes, and a Gigabyte is sometimes expressed in terms of Megabytes. Given that there are two possible definitions for Kilobyte (1,000 bytes or 1,024 bytes), two possible definitions for Megabyte (1,000 KB or 1,024 KB), and two possible definitions of Gigabyte (1,000 MB or 1,024 MB), the potential for confusion becomes exponential.

Hence, at the Gigabyte level, there are in fact 3² = 2 x 2 x 2 = 8 possible calculations for Gigabyte as follows:

Sometimes the resulting number of bytes is the same for different combinations, so the specific combination only matters if you are charged differently at each level (Kilobyte, Megabyte, Gigabyte etc). As demonstrated above, if binary and decimal definitions are used at different levels, there are two possible "pure" Gigabytes and two possible "hybrid" Gigabytes. Note that a purely binary Gigabyte is roughly 7% larger than a purely decimal Gigabyte.

The total number of combinations will increase to 16 as Terabyte PCs become more common, and a purely binary Terabyte (or "Tebibyte") is roughly 10% larger than a purely decimal Terabyte. Hence, as computing power and data storage capacity increase, so the issues are exacerbated exponentially (to the power of two) at each increase to the next level of bytes. And already the era of the Zettabyte is fast approaching (CISCO, 2008) - that's a billion times a billion times a billion bytes.

To add to the confusion you need to imagine the typical scenario of a file being uploaded or downloaded from one "computer" to another (and don't forget, these days "computer" typically means a server on the internet and your home computer, games console or mobile phone). The terms and conditions of your contract with your Internet Service Provider or telecommunications service provider might (if you're lucky) consistently specify data usage limits and excess data usage  charges in decimal kilobyte / megabyte / gigabyte terminology, whereas the files that you download / upload are typically tagged with a file size that is in binary kilobyte / megabyte / gigabyte terminology. This situation is analogous to the legal controversy (discussed later) over hard disk sizes expressed by manufacturers in decimal byte multiples but viewed through your operating system in binary byte multiples.

Your telecommunications or internet service provider is not normally responsible for highlighting or explaining this discrepancy. It is your responsibility to understand the implications, which are that your data usage typically doesn't allow you to download as much data as your terms and conditions specify, as binary bytes are bigger than decimal bytes. Hence you reach your data usage cap earlier than expected, and incur excess data usage charges earlier than expected too (unless of course your plan states no excess data usage charges).

On top of this confusion you can then add the terminology for bit rate and bandwidth which relates to data transfer rates and capacity which are expressed in bits not bytes and normally expressed in multiples of bits with SI Unit prefixes (usually meaning decimal not binary, but not always).

No wonder then that the International Electrotechnical Commission and the Institute of Electrical and Electronics Engineers (both eminent international standards bodies) have stepped in to standardise the terminology of binary bytes. It's a welcome development, to be sure.

However, because any kind of bytes (decimal or binary) are still excluded from the SI Units, governments around the world cannot easily incorporate the new standards into existing legislation for metrication and legal metrology and industry regulators are left impotent to enforce remote international standards. Thus, in the absence of any legal or regulatory obligations, manufacturers and service providers in both the telecommunications and information technology industries are at liberty to exploit such exponential confusion at the expense of the consumer.

With the rise of high definition video and digital cameras, it is now also quite common to hear the prefix "mega" applied to the pixel (kilopixels seemed to get skipped, and we're not yet ready for gigapixels). More pixels per image means more bytes in file size, so there is a direct relationship between the two. Pixels are also excluded from the SI Units, but we usually mean decimal megapixels not binary megapixels.

International Standards Relating to Bytes

As noted earlier, the BIPM gives its blessing to the first international standard designed to address the confusing terminology pertaining to "decimal bytes" and "binary bytes." - the International Electrotechnical Commission (IEC) standard IEC60027-2.

The IEC attempt to explain their position on their new standard (IEC, 2009), and it is clear that the IEC has high expectations:

"It eliminates confusion by setting out the prefixes and symbols for the binary, as opposed to decimal, multiples that most often apply in these fields."

The IEC make it abundantly clear that the "binary bytes" do not form part of the SI metric system (IEC, 2009):

"The new prefixes and symbols for binary multiples standardized in IEC 60027-2 are not part of the SI metric system of units."

Although the IT industry is not considered fully to blame by the IEC for the terminology confusion over bytes (the public and the telecommunication industry are also partly to blame), the IEC expects the IT industry to sort out the mess thanks to the development of the new IEC standard (IEC, 2009):

"In IEC 60027-2, all branches of the IT industry now have a tool with which to iron out inconsistency and achieve mathematical clarity as never before."

IEC60027-2 has since been superseded by ISO/IEC 80000 and joined by the Institute of Electrical and Electronics Engineers' IEEE 1541-2002 as a full standard in 2008. IEEE 1541-2002 is an IT industry standard that promotes the "binary bytes" terminology as standard for IT (Kibibyte, Mebibyte, Gibibyte etc).

In addition, the IEC standard was formally adopted by the European Union through the European Committee for Electrotechnical Standardization (CENELEC) Harmonization Document HD 60027-2:2003-03, meaning that binary bytes have formally standardised definitions available in the European Union nations.

CENELEC explains whilst a Harmonisation Document allows more flexibility than a full European Standard member states "... must also withdraw any conflicting standards" (CENELEC, 2009 [1]). You might be forgiven for thinking that this does away with the confusion over terminology for bytes in most of the European Union, but you'd be wrong. Firstly, there is no formal standard for decimal bytes anywhere. Hence, none of the member states can withdraw a conflicting standard if that standard never existed in the first place! Secondly, you need to understand CENELEC's mission (CENELEC, 2009 [2], my bolding):

"CENELEC's mission is to prepare voluntary electrotechnical standards that help develop the Single European Market/European Economic Area for electrical and electronic goods and services removing barriers to trade, creating new markets and cutting compliance costs."

So it would appear that the IEC's vision of a golden age of consistency and mathematical clarity for all is approaching and for Europe it is in theory at least already there if you voluntarily decide to use the new standard.

Issues with the IEC Position

There are a number of issues with the IEC position.

The word standard would imply that there is one set of terminology being recommended, yet the IEC, NIST and BIPM seem to acknowledge the continued use of "decimal bytes" as well as the preferred use of the new "binary bytes". So rather than having a single standard we now have a formally acknowledged dual standard. Even worse is that it is up to individual companies to decide which standard to apply for each multiple of bytes, and the same company can even vary their use of terminology depending upon the product or service being provided.

Another key issue with the IEC position is that, although binary bytes are explicitly excluded from the SI metric system of units (presumably because they are not metric), the IEC (and BIPM) are mute on the status of decimal bytes. However given the continued absence of decimal bytes from the SI metric system of units - the SI Units - and the lack of any endorsement for their inclusion into the SI Units it is clear that the IEC and BIPM do not support the inclusion of any type of bytes into the SI Units. Again, the IEC's reasons are unclear. Would it not be reasonable to include decimal bytes? Decimal Kilobytes are, after all, commonly understood in the same manner as kilograms and kilometres. It's a thousand of something. Or is it that bytes are simply not a unit of measure at all?

A massive practical issue is that, apart from the European Union nations, no other nation has formally adopted the new binary bytes standard. Also, even in those nations within the European Union that have now adopted the binary bytes standard, the new binary bytes standard is voluntary. There is no legislation that enforces binary bytes as a unit of measure, unit of information or unit of count.

Hence, in the absence of compulsory national standards for bytes, companies typically still use the SI Unit Prefixes for both decimal bytes and binary bytes, depending upon whether they're charging by the Kilobyte, Megabyte or Gigabyte.

ZDNet in the UK long ago noted the lack of appeal and lack of popularity of the new binary byte terminology, pointing out in 2002 only 454 Google hits for Gibibyte compared to 600,000 hits for Gigabyte (Goodwins, 2002). On 30th July 2009 I noted the following Google hit count for various terms pertaining to bytes:

So as competing memes, decimal byte terminology (with SI Unit prefixes) is massively more popular than binary byte terminology (with IEC prefixes). However, don't forget that whereas decimal byte terminology is being correctly used for decimal bytes, decimal byte terminology is also being abused for binary bytes and various hybrids of decimal and binary resulting is exponential confusion over "decimal byte" terminology as pointed out earlier. Without legislation and the equivalent of legal metrology for bytes it will be a long up hill struggle for IEC's new binary byte terminology.

Another issue is that it is naive of the IEC to expect all branches of the IT industry to eliminate confusion, iron out inconsistencies and achieve mathematical nirvana in this situation. Eliminate, or would reduce be more realistic? Who are all branches of the IT Industry anyway? Does this include manufacturers of mobile phones, games consoles (handheld or otherwise), DVD recorders, digital TVs, digital cameras, e-book readers, satellite navigation devices and MP3 players? Does the IT Industry include IT people working in every area of business, in defence, education, science, sport, gambling, music, health, journalism, telecommunications, and law enforcement? In at least one sense there is no separate IT Industry - in a developed nation IT is everywhere, in every office, every factory, every school and university, every hospital, every shop and every home. It is not up to the IT industry to solve this problem, it is up to organisations such as BIPM to incorporate the new standards into the SI framework so that existing laws for metrication and legal metrology all around the world can build upon the SI metric system of units.

What is so sacrosanct about the SI Units being metric anyway? They are a means to an end, not the end itself. Standards are there to facilitate our common understanding and encourage mutual trust in commerce and trade. So why not augment the SI metric system of units with binary bytes? Make just this one exception, and acknowledge the ubiquitous nature of binary-natured computers in the 21st century. Allow for both decimal bytes formally using the SI Unit Prefixes, and binary bytes using the new prefixes created by the IEC, noting if you like that bytes in either case are not a measurement but a count. Thus, bytes would become the first legal unit of count.

Note here that although the IEC seems to think that binary bytes "most often apply" no evidence of actual usage of binary and decimal bytes is offered by them. However, earlier in the same article the IEC contradicts itself and blames salesmen and the public for the popularity of decimal byte usage (IEC, 2009):

"Despite its inaccuracy and the inappropriate use of the decimal SI prefix, the term was also easy for salesmen and shops to use, and it caught on with the public."

The IEC itself notes that computers are inherently binary in nature but thanks to the efforts of organisations such as BIPM and the IEC itself in promoting the metric system, it is people and business who have grown comfortable with the metric system in general and applied it to bytes(and, more recently, pixels). If people and businesses want to continue to use decimal bytes why shouldn't they be able to do so? Thus, the expectation that the binary standard for bytes will just take over in the IT industry is itself naive.  People are not the IT industry, and the IT industry is not the people. Also, just because computers are binary it does not follow that people must refer to only binary bytes. It is perfectly simple to understand a decimal Kilobyte, Megabyte or Gigabyte.

Keep both decimal bytes and binary bytes

Therefore, although it is not ideal to legislate for a dual standard we must allow both standards to exist side by side, and legally force all manufacturers and service providers to consistently define which terminology is being used at all times:

Thus, whilst metrication and legal metrology go hand in glove and have presumably have been a boon to domestic and international trade, the whole can be considered as a framework already in place that can provide the legal leverage in every nation across the world to enforce the strict use of a legal unit of count for bytes.

A standard on its own lacks the legal status of legal metrology, both domestically and internationally. Should is not must. Standards are easily ignored if not backed up by the law. However, with a standard in place for clarification of terminology alongside the existing legal metrology framework of the SI metric system then the IEC's vision would be much more realistic.

The Situation in Australia

By way of an example, consider the situation regarding bytes in Australia today. If you are not from Australia, consider what you know about the situation in your own country.

Due to my prompting, the Australian Competition and Consumer Commission (ACCC) - responsible for the Trade Practices Act 1974 - issued a public warning which included the following statements (ACCC, 2004):

"Currently there is no actual standard in Australia. Two of the most commonly used are binary, which is when a megabyte (MB) measures 1024 kilobytes or decimal when a megabyte measures 1000 kilobytes. If you are unsure read your ISP's terms and conditions carefully. This also applies to mobile phone downloads and some computer hardware such as hard drives."

At the time I did try to persuade the ACCC to take things further under the deceptive and misleading conduct provisions of the Trade Practices Act 1974, but they were satisfied that telecommunications and IT industry definitions were clear enough. I have always disagreed with the ACCC, and will demonstrate that confusion over the terminology of bytes and the legal status of bytes persists today and even includes departments of the Australian Federal Government.

To date, Standards Australia have not formally adopted either ISO/IEC 80000 or IEEE 1541-2002. This would require either new legislation, or an amendment to existing legislation.

The National Measurement Institute (NMI) are responsible for legal metrology and metrication in Australia under the National Measurement Act 1960. The National Measurement Regulations 1999 further explain the application of the National Measurement Act 1960. Bytes are implicitly (but not explicitly) excluded from the NMI's responsibilities under the Act. It was explained to me by the NMI via email that bytes are not a unit of measurement, but a count, and that SI Unit Prefixes do not apply to bytes. The Act defines a unit of measurement as follows:

unit of measurement includes any word or expression that is used in conjunction with numerical values in order to describe the magnitudes of physical quantities.

The problem appears to be that bytes are virtual, and not physical. Thus, not only is there no standard  that applies in Australia, but there is no law that covers measurements (or even counts) of bytes described in numerous terms and conditions for various products or services.

The Telecommunications Industry Ombudsman (TIO) in Australia believes (TIO, 2001):

 "...that consistent definitions should be applied for all measurements, i.e. kilobytes, megabytes and gigabytes..."

even though the TIO is aware of one (unnamed) provider that mixes definitions using SI Unit prefixes for both "decimal bytes" and "binary bytes". The ombudsman seem completely unaware of the international standards available which, even though not formally adopted in Australia, could be promoted by the TIO if they chose to do so.

At my suggestion the Australian Communications Industry Forum (now a division of Communications Alliance Ltd) included the following in their industry code for consumer contracts (ACIF, 2005):

"Where a supplier uses terms such as kilobyte, megabyte, or gigabyte, the terms should be defined in the Contract and used consistently in the Contract and all collateral material, i.e. always using the decimal measurement or always using the binary measurement."

This industry code is available from the Australian Communications and Media Authority (ACMA) website. ACMA (the Australia's regulator for broadcasting, the internet, radio communications and telecommunications) has the following definitions in its Glossary:

There is no mention of even the possibility of binary bytes, with or without SI Unit Prefixes. However, these definitions are not a standard in Australia and are not legally binding on any manufacturer or service provider. These definitions are just ACMA's unenforceable opinion.

By way of a counter example to ACMA's definitions relating to bytes, consider these Australian Bureau of Statistics (ABS) definitions:

The Megabyte definition is not even very precise, especially for a government body and even more so given that it's the ABS we're considering here!

Even worse, it appears that the Australian Government's own e-Business glossary has these somewhat different definitions:

Note the highly dubious mixing of the binary standard at the Kilobyte level with the decimal definitions at the Megabyte and Gigabyte levels.

The use of the term "unit of measurement" is actually misleading here, as legal units of measurement as defined by the National Measurement Institute (NMI) in their responsibilities under the National Measurement Act 1960 does not include bytes. There are no legal units of measurement for bytes in Australia.

Furthermore, as noted by the IEC a floppy disk does not hold 1.44 million bytes it holds (1.44 x 1024 x 1000) = 1,474,560 bytes or 1.44 hybridised megabytes (IEC, 2009):

"...the capacity, originally described as 1 440 kB (kilobytes) before being 'translated' to 1,44 MB, is in fact a little over 2 % inaccurate because of the double misuse of a decimal prefix."

Finally the Australian Government might like to read the Wikipedia article on Gigabytes, in particular the section on consumer confusion, and similar sections in the article Binary Prefix. In short, although data capacity is often (but not always) defined in decimal byte terms the data file size itself is displayed by most common operating systems in binary byte terms. As noted above, binary bytes are bigger than their decimal cousins. An excellent white paper on the topic is available from Wiebetech (Wiebe, 2003). Hence it is dangerous to advise consumers viewing 700 MB of data (binary bytes) through their PC or Mac operating system  that this can fit onto a 700 MB CD-Rom (which are decimal bytes, according to the Australian Government).

According to the South Australian state government in their Information Economy article A Bit and a Byte:

References

This article makes extensive use of links to Wikipedia articles. Links to articles or websites not in Wikipedia are bolded.

Alder, Ken. The Measure Of All Things. Abacus. 2002.

ABS, Glossary, 8153.0 - Internet Activity, Australia, Jun 2008 (website accessed 27 July 2009)

ACIF, Industry Code - Consumer Contracts, ACIF620:2005, 2005 (website accessed 27 July 2009)

ACCC, August 2004 edition of Consumer Express (refer Bits & Bytes) (website accessed 27 July 2009)

BIPM, SI Brochure (8th ed.) (website accessed 27 July 2009)

BIPM-OIML-ILAC, "Joint Declaration", The relevance of various international agreements on metrology to trade, legislation and standardization (website accessed 9th August 2009)

CENELEC, CENELEC Deliverables, 2009 [1] (website accessed 27 July 2009)

CENELEC, About CENELEC, 2009 [2] (website accessed 31 July 2009)

CISCO, Approaching The Zettabyte Era. Cisco. 2008 (website accessed 13 August 2009)

Department of Industry, INFORMATION TECHNOLOGY INDUSTRY INNOVATION COUNCIL ESTABLISHED (Media Release, 05 May 2009), 2009 (website accessed 27 July 2009)

DBCDE, Unexpected high bills, 2009 [1] (website accessed 27 July 2009)

DBCDE, e-Strategy Glossary, 2009 [2] (website accessed 13 August 2009)

DBCDE, Australia's Digital Economy: Future Directions - Snapshot, 2009 [3] (website accessed 13 August 2009)

Goodwins, Robert. Binary finery: The forgotten standard that could save you money.ZDNet UK.  2002 (website accessed 31 July 2009)

IEC, When is a kilobyte a kibibyte? And an MB an MiB?, 2009 (website accessed 27 July 2009)

NMI,  How NMI contributes to Australia's economy, 2009 (website accessed 27 July 2009)

TIO - Gigabyte definition, 2001 (website accessed 27 July 2009)

Wiebe, James. When One Billion does not equal One Billion, or: Why your computer's disk drive capacity doesn't appear to match the stated capacity - A White Paper. Wiebetech. 2003 (website accessed 6 August 2009)

Send an email to dacoutts@optusnet.com.au with questions or comments about this web site.
Copyright 2009 David A. Coutts.

Last modified: 17 August, 2009