Copyright © 2008-2016 Exploring Binary
There is no widely accepted term for fractional binary numbers like 0.11001. A fractional decimal number like 0.427 is called a decimal or decimal fraction. A fractional binary number is called many things, including binary fraction, binary decimal, binary expansion, bicimal, binimal, binary radix fraction, and binary fractional (my term). In this article, I’m going to argue that bicimal should be the universal term.
(Please let me know what you think — take the poll at the end of this article.)
Why I Don’t Like ‘Binary Fraction’
Of all the existing terms, binary fraction is probably the most commonly used. I don’t like it because its analog, decimal fraction, is not clearly defined. I want to avoid a term that inherits this problem.
Decimal fraction is commonly defined as any number with an explicit or implicit power of ten denominator, either entirely fractional or not. For example, 254/1000, 0.254, 15/10, and 1.5 are decimal fractions. But what about 2/5? It can be written as 4/10 or 0.4, although as written its denominator is not a power of ten. And what about 1/3? Its equivalent form as a decimal is 0.3 — a repeating decimal. It can never be written with a power of ten denominator. To make things more confusing, 2/5 and 1/3 are fractions — fractions written in decimal numerals.
You could argue that decimal fraction includes 2/5 but excludes 1/3 and still have a reasonable definition. However, I’m looking for the equivalent of decimal, a term which includes 0.4 and 0.3, but excludes 2/5, 4/10, and 1/3.
I discovered the term bicimal on the Web and in Google Books, but I don’t know its origin. I pronounce it “bye’ suh mull”, or as Merriam-Webster might express it, \ˈbī-sə-məl\. A bicimal is built with negative powers of two, whereas a decimal is built with negative powers of ten.
Like the term decimal, bicimal usually means a pure fractional value, like 0.11001. However, in some contexts, it could mean numbers with a whole and fractional part, like 101.11. In this case, nonnegative powers of two come into play — for the whole part.
Why I Like ‘Bicimal’
Ideally, there would be a base-independent term for the fractional part of a number. I invented the term fractional for this purpose. I’ve called a fractional decimal number a decimal fractional, and a fractional binary number a binary fractional. The purpose of this new term was to separate the form of a number — a number with a “point” in it — from its base. If 0.427 is a decimal, does that make 0.11001 a binary decimal? You can see why we need a better term.
One problem with my terminology is that I’ve created two terms (decimal fractional and binary fractional) when I really only needed to create one. Why not stick with decimal and invent a new term just for binary? Decimal is easier to say than decimal fractional, and everyone knows what it means. So what’s a good replacement for binary fractional? I’ve come to like the term bicimal.
At first glance, there’s not much to like about bicimal. It’s base-dependent, and it is a portmanteau for binary decimal. It is a poorly formed portmanteau at that. While the prefix ‘bi-’ is perfectly acceptable, its pairing with the suffix ‘-cimal’ seems ill-formed. Binimal seems linguistically the better choice; it swaps out the prefix ‘dec-’ for the prefix ‘bin-’ and retains the suffix ‘-imal’.
On the other hand, say bicimal and binimal outloud, over and over; I think you’ll find that bicimal sounds better, as do its associated terms: bicimal point, bicimal places, bicimal part, terminating bicimal, repeating bicimal, infinite bicimal, etc. And bicimal produces natural sounding phrases like “multiply bicimals”, “convert a decimal to a bicimal”, “convert a bicimal to a decimal”, “convert a bicimal to a fraction”, “convert a fraction to a bicimal”, etc.
I think bicimals will be immediately understood by newcomers. It evokes all the feelings and terminology and operations of decimals (for better or worse :)). I don’t think binimals — or any of the alternative terms — has this property. So all things considered, I like bicimal the best.
What Do You Think?