Transliteration of Numbers of an Arbitrary Base>>  Click to open

A post on Slashdot asked the question, how does one transliterate numbers of arbitrary bases? For example the number "562" is transliterated as "five hundred sixty two" but how would one transliterate the hex number "0xDEADBEEF"?

The text below attempts to answer that question using two methods. The first is a rigorous and technically accurate method but is difficult to use. The second is technically less rigorous but is simple to use.

Introduction to American and European Numeric Transliteration

Methods of transliterating numbers from their written form to thier spoken form employ two distinct structures. The first is several unique power-of-ten suffixes appended to individual root-word digits and the second is an incremental multiplier added to groups of numbers in powers of 10³.

The unique power-of-ten suffixes are as follows.

Value	Suffix	Example	Notes
100	-	seven	No ending
101	-ty	seventy	10-12, 20, and 30 are irregular
102	-hundred	seven hundred

The incremental modifiers represent powers of 10³ or in the case of European incremental modifiers, powers of 10⁶ in conjunction with "thousand."

Value	American	European
100	-	-
103	thousand	thousand
106	million	million
109	billion	thousand million
1012	trillion	billion
1015	quadrillion	thousand billion
1018	quintillion	trillion

Note that the values represented by American incremental modifiers are derived by taking the numeric prefix of the transliteration, adding one, multiplying the result by three, then taking ten to that power. Thus one trillion is 10⁽³⁺¹⁾³ or 10¹². The European convention uses latin prefixes to denote powers of a million. Thus in Europe one billion is (10⁶)² or 10¹², which is equal to a trillion using American conventions.

In summary, the American system employs three suffixes for the ones, tens, and hundreds place with a unique incremental modifier used for multiples of 10³. The European system also uses three suffixes for the ones, tens, and hundreds place but places a unique incremental modifier only at multiples of 10⁶. Because only three suffixes are employed in the European transliteration scheme (instead of six to span 10⁶) the first three suffixes are reused by collectively multiplying groups by the modifier "thousand." This allows the three unique suffixes to span the required range of 10⁶.

Using the American methodology, the number "785,391,247,462" is transliterated as follows. Using the European methodology, the number is transliterated as follows. What's interesting to note, is that the value of the incremental modifier is arbitrary. Americans use 10³, Europeans use 10⁶, and Japanese use 10⁴ (more on that to follow).

Method I: Technically Accurate but Difficult

Thus to answer the question of how to transliterate numbers of an arbitrary base, we must simply define the standard suffixes, define a method for constructing incremental modifiers, and settle on a size of the multiplier.

I suggest the selection of B³ as the value of the incremental modifier's multiplier, where B represents the base number. It will minimize the number of suffixes required, while avoiding the complication of including an additional multiplier to span large values (as in the European system). Given that, only three repeating suffixes and a system of naming incremental modifiers based on powers of B³ are required.

For the three repeating suffixes, I suggest a naming scheme based on genitive Latin ordinal numbers, where that ordinal corresponds to the power of the base and can be translated as "of the n^th."

Value	Latin	Suffix
B0	nulli	-
B1	primi	-primi
B2	secundi	-secundi

Note that the first suffix is omitted as in English (and other European languages). The suffix for B¹ is "-primi" and the suffix for B² is "-secundi." As an example, the number "145," transliterated, using base-ten-specific naming conventions as "one hundred fourty five," would be transliterated using the base-generic method as "one secundi fourprimi five." (Awkward? Stay tuned. I'm just getting started.)

As stated above, the incremental modifier has been selected to be a multiple of B³. To represent that value, the root word "trigarium," meaning "team of three horses" in Latin, has been selected. Additional incremental modifiers are simply constructed by adding Latin numerical prefixes.

Value	Latin	Abbreviation
B3	trigarium	trig
B6	bitrigarium	bitrig
B9	tritrigarium	tritrig
B12	quadtrigarium	quadtrig
B15	quinttrigarium	quinttrig
B18	sextrigarium	sextrig
B21	septtrigarium	septtrig

Using this system, the hex number "0xDEADBEEF" transliterates as follows.
It's absolutely gibberish-tastic!

Method II: Technically Inaccurate but Easy to Use

The second method simply steals all endings from the existing base-ten transliteration method. Provided that the base is made clear, there's no chance of error. I mean, how many of us really use MiB instead of MB? Using this simpler system, the hex number "0xDEADBEEF" transliterates as follows.
And that's all I have to say about that.

Copyright © 2008 Michael Forman

This is the sort of English up with which I will not put. -- Winston Churchill