Taking the measure of unit qualifiers - Embedded.com

Taking the measure of unit qualifiers

Recently, I was in an email conversation with one of the editors at Everyday Practical Electronics (EPE) , which is the UK's premier electronics and computing hobbyist magazine. (There used to be two magazines — Practical Electronics and Everyday Electronics — but they merged many years ago; hence the EPE moniker.)

Anyway, my friend at EPE shared a “Letter to the Editor” with me, part of which read as follows:

It interests me that in your article you use the prefix “k” for kilo. I was always taught throughout school and university (albeit a long, long time ago!) that any prefix larger than the unit must be in uppercase and smaller in the lowercase; for example, Mm is megametre and mm is millimeter; likewise Dm is decametre whereas dm would be decimetere; therefore kilometer should be Km.

This is one of those perennial topics that keeps on coming back to haunt us. Let's start with the fact that the metric system of measurement was developed during the French Revolution and its use was legalized in the US in 1866. The International System of Units (SI, which stands for Système International d'Unités ) is a modernized version of the original metric system.

Stop! It Hertz!
In the case of an SI unit that is derived from the proper name of a person, the first (often only) letter of its symbol must be in uppercase, while any other letters are in lowercase; for example V, A, W, F, H, and Hz, which stand for “volt,” “amp,” “watt,” “farad,” “henry,” and “hertz,” respectively. By comparison, when this type of SI unit is spelled out in English, it should always begin with a lowercase letter (volt , amp , watt, farad , henry , hertz , etc.), except when used at the beginning of a sentence or in capitalized material such as a title.

As an aside — and just in case you were wondering — the term volt is named after the Italian physicist Count Alessandro Giuseppe Antonio Anastastio Volta (1745–1827), who invented the electric battery in 1800. (Having said this, some people believe that an ancient copper-lined jar found in an Egyptian pyramid was in fact a primitive battery used for electroplating… but, there again, some people will believe anything. Who knows for sure?) Meanwhile, the terms amp and ampere are named after the French mathematician and physicist André-Marie Ampère (1775–1836), who formulated one of the basic laws of electromagnetism in 1820. An amp corresponds to approximately 6,250,000,000,000,000,000 electrons per second flowing past a given point in an electrical circuit.

But wait… there's more! The amount of power consumed by an electronic circuit is measured in watts , where the term watt is named after the Scottish inventor and engineer James Watt (1736–1819), whose improvements to the steam engine were fundamental to the changes brought by the Industrial Revolution. The term farad is named after the British scientist Michael Faraday (1791–1867), who constructed the first electric motor in 1821. The term henry is named after the American inventor Joseph Henry (1797–1878), who discovered inductance in 1832. And the term hertz is a unit of frequency, where one hertz equals one cycle — or one oscillation — per second. The hertz is named after the German physicist Heinrich Hertz (1857–1894), who made many important scientific contributions to electromagnetism.

Little and large
Electronic engineers often work with very large or very small values of voltage, current, resistance, capacitance, inductance, and so forth. As an alternative to writing endless zeros, electrical quantities can be annotated with the qualifiers given in the table shown below.

For example, 15 MO (15 megaohms) means fifteen million ohms, 4 mA (4 milliamps) means four thousandths of an amp, and 20 fF (20 femtofarads) means a very small capacitance indeed.

Since I love trivia, there are several things worth noting about this table. In Britain, for example, the term billion traditionally used to mean “a million million” (10^12). However, for reasons unknown, the Americans decided that billion should mean “a thousand million” (10^9). In order to avoid the confusion that would otherwise ensue, most countries in the world (including Britain) have decided to go along with the Americans on this one.

The term giga (G) comes from the Greek gigas , meaning “giant”; the term mega (M) comes from the Greek mega , meaning “great” (hence the fact that Alexander the Great was known as Alexandros Megos in those days of yore); and the term kilo (k) comes from the Greek khiloi , meaning “thousand.”

Personally, I agree with the writer of the letter in that I think it would make more sense for every qualifier larger than unity to be in uppercase, while every qualifier smaller than unity would be in lowercase. In fact, this is largely the way things are; for example we have mega = 10^6 = M, giga = 10^9 = G, tera = 10^12 = T, peta = 10^15 = P, exa = 10^18 = E, zetta = 10^21 = Z, and yotta = 10^24 = Y. Similarly, we have milli = 10^-3 = m, micro = 10^-6 = u or µ, nano = 10^-9 = n, pico = 10^-12 = p, femto = 10^-15 = f, atto = 10^-18 = a, zepto = 10^-21 = z, and yocto = 10^-24 = y.

So why do we use a lowercase 'k' for kilo? Well, one reason is that the uppercase 'K' is reserved for “Kelvin” — the fundamental unit of temperature — which was named for the great physicist and engineer Lord Kelvin, who was Professor of Natural Philosophy for over 50 years at Glasgow University.

It's also worth noting that the lowercase 'k' is not alone; currently, hecta (also spelled hecto ) (h) and deca (also spelled deka ) (da) are also lowercase. (In the not-so-distant past, the prefixes hecto, deca, deci, and centi were commonly used for everyday purposes; the use of centimeter (cm) is still common.) The reason I used the “currently” qualifier is that the system is updated and refined from time to time. Prior to 1960, the now-little-used deca had a confusing variety of prefixes, such as dk, D, and Da. Some old cooking books specified weights in decagrams (Dg), for example, but today's decagramophiles would use dag .

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Bits and Bytes
Sometime in the late 1940s, the American chemist-turned-topologist-turned-statistician John Wilder Tukey (1915-2000) realized that computers and the binary number system were destined to become important. In addition to coining the word “software,” Tukey decided that saying “binary digit” was a bit of a mouthful, so he started to look for an alternative. He considered a variety of options like binit and bigit , but he eventually settled on bit , which is elegant in its simplicity and is used to this day.

The term byte was coined by the American computer scientist Werner Buchholz in 1956, and is a deliberate respelling of “bite” to avoid accidental mutation to “bit.” Historically, a byte was the number of bits used to encode a single character of text in a computer. For this reason, the size of a byte used to be hardware dependent with no definitive standard that mandated the size. Over time, the de facto standard of an 8-bit byte emerged, and this was codified in a formal standard with ISO/IEC 80000-13.

As yet another aside, a group of four bits is commonly referred to as a nybble (or “nibble”). “Two nybbles make a byte” is an engineer's idea of a joke, which shows that engineers do have a sense of humor (it's just not a particularly sophisticated one). Continuing the theme, there have been sporadic attempts to construct terms for bit-groups of other sizes; for example, tayste or crumb for a 2-bit group, playte or chawmp for a 16-bit group, dynner or gawble for a 32-bit group, and tayble for a 64-bit group.

But you can only take a joke so far, and using anything other than the standard terms nybble and byte is extremely rare. Having said this, the term word is commonly employed in the context of electronic systems to represent the natural unit of data used by a particular processor or sub-system; the size of a word (which may be referred to as word size , word width , or word length ) is defined by each system's internal architecture.

Thanks for the memory
Another source of confusion for anyone working in electronics is the kilobyte. Standard memory devices are constrained to have a depth of 2^n words. In SI units, kilo (k) represents one thousand (1,000), but the closest power of two to one thousand is 2^10, which equals 1,024. Similarly, mega (M) typically represents one million (1,000,000), but the closest power of two to one million is 2^20, which equals 1,048,576.

The point is that, when people are writing about computer memory, they typically use an uppercase K for kilo. Meanwhile, a lowercase 'b' is used to represent “bit” while an uppercase 'B' is used to represent “byte,” which leads to us using “Kb” for kilobit and “KB” for kilobyte and “Mb” for megabit and “MB” for megabyte, etc.

The use of the standard SI qualifiers k, M, G, etc., to designate exponents of two in electronic systems has always been a misuse of these terms, leading to endless confusion among the uninitiated. In order to address this problem, the International Electrotechnical Commission (IEC) established a new set of units in 1999 (see the Binary Prefix topic on the Wikipedia and scroll down to the section marked “Specific units of IEC 60027-2 A.2 and ISO/IEC 80000”). These units are shown in the table below:

Apart from anything else, this IEC standard uses an uppercase 'K' in “KiB,” which makes it worth its weight in gold with regard to addressing the 'k' versus 'K' debate and removing confusion and frustration in this area.

These new units have been accepted for use by all major standards organizations. Having said this, they have seen little adoption outside the computer industry (or even inside the computer industry, for that matter), but their use is growing.

There's no space!
Instead of writing “5 volts,” engineers would typically abbreviate this to 5V. Similarly, instead of writing “0.5 amps,” engineers would typically abbreviate this to 0.5A. Also, the Greek letter omega 'Ω' is used to represent resistance, so instead of writing “10 ohms,” engineers would typically abbreviate this to 10Ω. [The term ohm is named after the German physicist Georg Simon Ohm (1789–1854), who defined the relationship between voltage, current, and resistance in 1827 (we now call this Ohm's Law ).]

Observe that no space is used in the case of a single-letter unit qualifier like 0.5A (or 10Ω), but a space is required when using a multi-letter unit qualifier such as 500 mA, where 'm' stands for milli , meaning “thousandth,” as discussed earlier. Having said this, in certain cases — such as discussing integrated circuit technology nodes and the size of memories in electronic systems — it's very common to see folks writing stuff like 28nm (meaning “28 nanometers”) and 64MB (meaning “64 megabytes”) without a space.

Purists would say that just because lots of folks do something doesn't make it right, but personally, I think that there are more important things to worry about. On this basis, I'd say that what you decide to do in these cases is up to you; the most important thing here is to be consistent; i.e., don't use 28nm in one part of a document and 28 nm somewhere else, because that really gets up my nose wears on the readers' nerves.

Furlongs, firkins, and fortnights
A furlong is a unit of length (one furlong equals 660 feet); a firkin is a unit of mass (one firkin equals 90 pounds); and a fortnight is a unit of time (one fortnight equals two weeks or fourteen days). The point is that if you were reading a paper and you saw something like 1 fpf, it's doubtful that you would immediately leap to the conclusion that the author was trying to convey the concept of “One furlong per fortnight” (which actually equates to approximately 1 centimeter per minute).

The thing is that I get to read a lot of scientific and technical papers, and it really wears on my nerves when an author uses some unit of measure that may well be de rigueur in certain circles, but that is unfamiliar to yours truly (see also The Smoot and The Potrzebie System of Measurement).

On this basis, in my own writings, if I move outside the most basic of units, then I spell things out on first usage; for example, I might write “10 Gbps (gigabits per second),” the first time I use the “Gbps” qualifier, just to ensure that we're all tap-dancing to the same drum beat.

Well, I'm glad I got all of that off my chest. I personally think this sort of thing is rather interesting, with enough and tidbits of trivia to keep me amused for hours. Speaking of which, if you have any unit – and/or unit qualifier -related nuggets of knowledge, please share them with the rest of us in the comments below.

42 thoughts on “Taking the measure of unit qualifiers

  1. “Computing lore has nevertheless assigned a distinction (particularly in reference to memory) between kB and KB as 1000 bytes and 1024 bytes, respectively – the latter having “… originated as compromise jargon….” according to the relevant wikipedia e

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  2. “MaxnnWhen I was in university in Israel in the early 70s, they followed what I believe was the European terminology- a milliard was an American billion and a billion was the English billion.”

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  3. “In computer science the norm is to use lower case 'i' to designate use of radix 1024 instead of ten. I.e. kiB vs kB, MiB(sigh) vs MB GiB vs. GB and so on …”

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  4. “Then you have the financial community who will use the Roman numeral M, meaning 1000 to express one million dollars as $1MM, which any engineer would instantly interpret as meaning 10^12 dollars and wonder why they didn't just write $1G.”

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  5. “Good grief — this is a new one on me (not the fact that the Roman numeral M represents 1000 — the fact that the foolish financial folks use MM to represent 1,000,000) — there's always something new to learn, isn't there?”

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  6. “One of the nice things about the American version of the English language is that, while rules are taught in school, by convention, there really aren't any rules. If you don't like something, make up your own spelling, grammar, or rules of any sort.nnAn

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  7. “I'm assuming you're talking about the fact that the American Pint and Gallon are smaller than their Imperial (English) counterparts?”

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  8. “Yes, and English is somewhat backwards compared to most other languages, where the action is saved till the end of a sentence. That's what made Yoda-speak so charming (or annoying to some I suppose). With such heavy French and German influences, I guess i

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  9. “Years ago when I first started working for Motorola, someone must have thought it was too hard to convert between mils and microns (1 mil = 25.4 microns). This conversion was need to switch between IC layout dimensions (microns) and Gerber rubilith dimens

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  10. “I see that they add a space even for a single letter qualifier like 10 W, while I said it should be 10W. I still think I'm right LOL”

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  11. “I looked further into the list- there re some great ones, but the on I found the most amusing was:nnBeauty: Helen[edit]nnMain article: Helen (unit)nnHelen of Troy (from the Iliad) is widely known as “the face that launched a thousand ships”. Thus,

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  12. “I love this stuff — and I'm always amazed at how creative people are — I wish I could come up with something half this clever.”

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  13. “Max,nnIn order to deduce confusion and ambiguity, I believe that all writers should abide by the SI standards. NIST is the repository and interpreter for such things in the US. NIST has (www.nist.gov) two pdf publications (SP811 and SP330) that cover th

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  14. “Hi Doug — on the one hand I do agree with you — I also like that saying “Standards are great… everybody should have one” LOL.nnHaving said this, I also have a sneaking agreement with the philosophy that “Rules are for the guidance of wise men and

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  15. “Really, no one is going to start with the puns? There was a whole list of them once, but somehow the only one I can remember is the one I made up (and which is thus of unvetted humor quality):nn2E6 microscope = 1 periscope”

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  16. “Hello everyone, my name is Wendy Blizz here is the testimony of my life, is unbelievable. Never knew people like dr.amigo still exist this shock me up till now. My hubby left me for another woman after 2years of marriage, i was heart broken I lost my job

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  17. “”My hubby left me for another woman after 2 years of marriage…”nnPossibly because you are prone to posting totally irrelevant comments on technical forums where they will be read by people who really could care less about your meaningless meandering

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  18. “I have to say that the more I learn about different languages, the more I am amazed about how many different ways there are to do things. Having said this, English is obviously the best, otherwise I wouldn't have devoted so much time and effort to learnin

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  19. “When NASA first started putting tiny attitude correction thrusters on space suits, each “puff” from a thruster was called a “Mouse fart”. I think it's fair to use that as a unit of measure.nnAnd while we're on the subject of mice, the smallest dete

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  20. “Here's another I've just remembered – not a unit per se, more like a remarkable fact which (as usual) I don't really remember where I heard:nto within 0.1%, pi seconds is a nanocentury.”

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  21. “Several notes:nnu2022 On the long scale (10^12, 10^18, u2026) versus short scale (10^9, 10^12, u2026) interpretation of billion, trillion, u2026: Most English-speaking countries and Arabic-speaking in the world (including Britain) have decided to go

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  24. “Several notes:nnu2022 On the long scale (10^12, 10^18, u2026) versus short scale (10^9, 10^12, u2026) interpretation of billion, trillion, u2026: Most English-speaking countries and Arabic-speaking in the world (including Britain) have decided to go

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  25. “Eeek — you are correct — I just went back in and “tweaked” this — thanks for spotting it and for letting me know — thanks also for the kind words.”

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  26. “Then there is the “Attoboy” which the boss sometimes gives to successful employees. But beware, it takes only a single “Oh 5#1+!” to cancel 1000 Attoboys.”

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