If you want great precision, a fractional system will always be better. A
fraction by definition can express any rational number with perfect
precision. A decimal is much more limited. For example, you cannot express
1/3 in decimal with perfect precision, at least not using a finite number of
digits. When used in calculations, decimals can and will accumulate errors,
and sometimes the result can be wildly different than the true answer even
after just a few steps. Correctly identifying and handling accumulation of
errors in floating point arithmetic (like decimal, but usually using a
binary number system) is a very difficult and complex area in computer
The metric system is generally considered better for two reasons:
1) It is much more rigorously standardized conceptually. Every unit is,
obviously, based on multiplication or division of 10. A kilogram and
kilometer is a multiple of 10 (i.e. 1000) of a gram and meter, respectively.
And this applies to all types of measurements--length, volume, area, mass,
etc. It's much easier to translate, e.g., lengths into area as the
conversion factors are typically much simpler. Even the names of units are
standardized: kilo-, milli-, etc.
2) Arithmetic with decimals is also much simpler because it's similar to
regular arithmetic with whole numbers. Calculating with fractions requires
more book keeping. The most common calculations are pretty simple in US
customary units, but in science and engineering you're often dealing with
arbitrary numbers with much more precision. IOW, you're not always or even
rarely juggling standard dimensions that co-evolved to work well with common
sums and multiples.
That doesn't mean metric is the best possible choice. Base-10 is a really
crappy multiple. It's an historical accident that we use it, and it has
nothing to do with the number of fingers we have. Units of 10 cannot express
very well 3rds or even 4ths. People undoubtedly still conceptualize those
things as fractions even when using decimal. Arguably we'd be better off
using base-12, or even base-60 like the Babylonians. 12 is evenly divisible
by 2, 3, 4, and 6. 60 is divisible by 1, 2, 3, 4, 5, 6, 10, 12. People are
already familiar with base-12 and base-60 units as it's how we count time.
And some other familiar measurements loosely (but inconsistently) utilize
those units. (We still express those units using decimal notation, though,
which can be confusing.)
Computer science uses base-2 (binary) because of similar properties related
to how arithmetic works. Base-8 (octal) and especially Base-16 (hexadecimal)
is common in software. The former makes it more intuitive to work with
groups of 3 in the context of binary numbers, while the latter makes it more
intuitive to work in groups of 2, 4, and 8. You can get used to thinking in
different bases fairly easily. I think math would come easier for many young
kids if they practiced using different number systems explicitly. I never
really "got" English grammar (beyond rote memorization) until I began
learning Spanish in high school. Spanish class did more to help me
understand English grammar than any English class ever did.
Good post, well thought out and presented
I thought, though, that CS used base-2 because that was what the hardware
did. As I understand transistors and TTL, they natively work with the
presence or absence of a voltage, which lends itself to base-2.
Base 8 and 16 are "shorthand" for base 2.
e.g. 14 (Decimal) = 1110 (base 2) = 16 (base 8) = E (base 16).
People don't like 0s and 1s, but computers do, so we have software that
translates between various bases. Of course 14 need not just be an
numeric value, it could also represent an instruction which tells a
computer to increment a register, or to do some other thing.
Forgot a popular number base - Icono hexadecimal Base 26.
Used the alphabet and numbers. This was for large 64 bit and 128 bit
parallel processors for the military and used in the 360 by some.
Last I heard, the military division of IBM was closed down.
On 9/14/2016 7:37 PM, Bill wrote:
HomeOwnersHub.com is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here.
All logos and trade names are the property of their respective owners.