West-East Notation & Bin Notation

West-East Notation: A Scientific Notation Easier to Type and Pronounce

Bin Notation: An Alternative to SI Binary Prefixes

Summary/Abstract:

Let $$x$$e$$y$$ mean $$x \cdot 10^y$$, e.g. 5.78e3 = $$5.78 \cdot 10^3$$.

Let $$x$$w$$y$$ mean $$x \cdot 10^{-y}$$(=$$x \cdot 0.1^y$$), e.g. 5.78w3 = $$5.78 \cdot 10^{-3}$$(=$$5.78 \cdot 0.1^3$$).

Let $$x$$B$$y$$ mean $$x \cdot 1024^y$$, e.g. 5.78B3 = $$5.78 \cdot 1024^3$$.

Let $$x$$b$$y$$ mean $$x \cdot 1024^{-y}$$ e.g. 5.78b3 = $$5.78 \cdot 1024^{-3}$$.

Pronounce (in all languages) “e” as “east”, “w” as “west”, “B” as “bin”, “b” as “subbin”.

Keywords:

west-east notation; bin notation; scientific notation; exponential notation; E notation; SI prefixes; binary prefixes.

1. Introduction

The traditional scientific notation is not available in text editors, and even in word processors it is time-consuming to write a number in this notation, because:

(i) we need the multiplication symbol (a centered dot or a cross), which usually is not in the basic character set and requires special tools (such as the Character Map) to be inserted, and

(ii) we need to enable the superscript and to disable it after typing the exponent.

Also when read aloud, a number in the scientific notation involves quite a long phrase “times ten to” (3 syllables; or 5 syllables in the Polish language, for example).

2. West-East Notation: A Scientific Notation Easier to Type and Pronounce

Here is an idea taken from computers and calculators. When a number in the scientific notation is entered, printed or displayed, the letter “E” or “e” stands for “times ten to”. For example 5.78E3 means $$5.78 \cdot 10^3$$. This is known as the E-notation; unfortunately this notation is not encouraged in some publications, see [2].

E-notation has disadvantages:

- “5E3” can be understood as “5.3 exa”: “E” is the symbol of the multiplicative prefix “exa”, equal to $$10^{18}$$; some people write a multiplicative prefix symbol instead of the decimal point (this is officially accepted for kilo and mega, as yet).

- “5.78E-3” can be understood as “five dot seventy eight times E subtract three”.

- In speech: “five dot seventy eight E three” can be understood as “5.78 times $$E_3$$”.

I propose to modify E-notation in several ways which avoid these vices – may be my version will be accepted in publications and on conferences.

Firstly, use lowercase “e” to avoid the confusion with exa. (In many calculators, including MS Windows application “Calculator”, lowercase “e” is used.)

Secondly, to avoid the confusion in speech, the “e” should be pronounced as “east”, rather than as “ee”. This pronunciation corresponds well to moving the decimal point towards the right (because east is at the right-hand side of most maps).

Thirdly, the phrase “east minus” is still too long for comfortable speaking – so let us replace it by “west” (and the letter “w”); for example 5.78w3 should be read “five dot seventy eight west three”, 5.78w3 = $$5.78 \cdot 10^{-3}=5.78 \cdot 0.1^3=0.00578$$. This corresponds to moving the decimal point towards the left.

Once “w” is introduced, we may decide to use “e” and “w” only with unsigned numbers (i.e. non-negative integer numbers, without the “+” sign) as $$y$$ (see Summary above). This would prevent confusion with a variable “e” or with the mathematical constant e=2,71828..., which are never followed directly by a number without any intervening arithmetic operator.

And a request for constructors of calculators (including computer applications Calculator): please make a button to denormalize a number in exponential notation by moving the decimal point towards right and decrement the exponent. And a button (maybe the same button prefixed by 2nd or INV) for the opposite operation. In 70-ties Texas Instruments produced calculators TI-30 and SR-40, which had this function, especially useful if one wants to replace the exponent by an SI prefix; the button was labelled EE↓ and the same button anteceded entering the exponent when typing a number in scientific notation.

3. Bin Notation: An Alternative to SI Binary Prefixes

In the computer technology, powers of 1024 are in common use and prefixes M (mega), G (giga) and higher are used in an ambiguous way: $$M = 10^6$$ or $$M = 1024^2$$, $$G = 10^9$$ or $$G = 1024^3$$, etc. The International Electrotechnical Commission introduced SI binary prefixes in 1998 (IEC 60027-2 standard, [1]), but they are still not popular. Maybe the following alternative will be accepted by the community.

Let's introduce “B” in a similar way as “e” and “w”: $$x$$B$$y$$ = $$x \cdot 1024^y $$. Read this “B” as “bin”, for example 5.78B3 should be read “five dot seventy eight bin three”. For the sake of completeness:  $$x$$b$$y$$  = $$x \cdot 1024^{-y}$$; “b” should be pronounced as “subbin”, for example 5.78b3 should be read “five dot seventy eight subbin three”. If “subbin” were not introduced, perhaps somebody would say: Bin Notation leads to ambiguity,  e.g. 5.78B-3 might be understood as 5.78 times variable B subtract 3. However, expressions $$x$$b$$y$$ are highly unlikely ever to be used. In most descriptions of binary SI prefixes, submultiples are not listed at all.

References:

[1] IEEE Std 1541-2002: IEEE Trial-Use Standard for Prefixes for Binary Multiples, 12 February 2003. doi:10.1109/IEEESTD.2003.94236. Print ISBN 0-7381-3385-X, Online ISBN: 0-7381-3386-8. (or Wikipedia, article Binary prefix.)

[2] Edwards, John (2009), Submission Guidelines for Authors: HPS 2010 Midyear Proceedings (PDF), McLean, Virginia: Health Physics Society, p. 5.