Decimal number system

[Comraddict]

Why we still use this aboslutelly imperfect numeric system? It was developed long time ago before binary, hex and oct. systems were known.
What is so magic that we count numbers 1 to 9?
Why not 1 to 7?
Question is..would be everything easier if we use "natural" system with base of 2?

 

[Immortal]

you will have to be more descriptive.

 

[Comraddict]

It is maybe hard to explain why base 2 is better than base 10.
Base 10 is useless in nature. Base 2 is perfect for computers and machine calculations. Wth that anology, I come to conclusion it would be easier for humans to work with perfect base of two, or eight, which is still 2 on power of three..

 

[Stile]

Fewer characters to represent a number. For instance here is the population of the US in base 2: 10000101100000111011000000000.

A little unwieldy? Base 8 is a decent way to represent Base 2, but let's face it we have 10 fingers and it seems like a waste to not include our thumbs. That's the real reason.

 

[Double Barrel]

But...but...we've got 10 fingers!

 

[Maj]

I wonder why the Gauls used base 12 ...

What's rational and logical may not be practical. An example would be the American and British adherence to the Imperial system of measurement. Although the sciences in those countries have adopted the metric system the general populace sticks to their familiar miles, pounds and gallons. The change may help them solve arithmetic problems dealing with measured quantities, but the math they'll most be interested in is the immense cost of implementing metric. The cost would far outweigh the benefits.

 

[Lefty Scaevola]

Number of fingers. Babylonians and Gauls that had base 12 likely had a king or great scholar of with extra fingers at the time they codified a numerical system.

 

[sysyphus]

Perhaps someone ought to invent the decimal computer. I'm sure it's not an impossible situation to develop an electronic device that holds 10 states instead of 2.

For logical operations, could simply mean the if the bit under concern is 0-4 then it is "low" and if it is 5-9 then it is "high"

Such a computer would proably be more effecient since there'd be fewer bit operations to execute a single instruction.

Of course, since we're already on the binary standard, such a change would be way too big to implement.

 

[Comraddict]

I think it is impossible to invent 10 reliable states. All electronics still have problem to correctly identify states 0V and 5V ( 0, 1). Very often signal comes near line that sepratates states - lets say 2.5V.
Transistors, as a base of all electronics, are very non -linear devices. Basically they do have only two states- enough voltage on collector- passing or not enough voltage od collector- blocking

 

[sysyphus]

That's the current use of digital electronics, but analogue sytems have been around for much longer, and an integration of analogue electronics into computer systems could make it work.

Remember also that computer values are stored on capacitors, not transistors. The technology of the storage has come a long way, and realising it into 10 states is an advance I could envision possible before too long.

Transistors are only used in switching operations, thus my suggestion that for logical ops, 0-4 and 5-9 gives plenty of breathing room for those.

By replacing mathematical operations which are currently done with binary logic systems instead with analogue systems it's much more feasible. Analogue amplifiers are not susceptible to the non-linearity of transitors.

 

[nihilistic]

Well ... you see, we have grown used to decimal. And not only have we grown used to decimal, it really cannot be demonstrated how other systems are superior or inferior to decimal to an extent where either it must be replaced or further appraisal must be given. I myself can actually convert between binary, octal, hex, and decimal freely, but I 'm also better in math than the vast majority of peopole I know. There is nothing too terribly wrong with the decimal system, so I will invoke the paradim of "If It Ain't Broke Don't Fix It".

On a side note though, I'll present a simplistic analysis of number base systems: Theoritically, the euler constant 'e' should be the optimal base, but we don't use 'e' because we like to think of whole numbers. In theoritical computer science, 3 might arguably be an optimal base since it is both absolutely and logarithmically the closest integer to 'e'. In practice, base 2 seems simpler for logical computation since logical statements (where allowed) only has two states (true or false).

However, both binary and ternery are way too tedious for us humans. In binary for particular, it is very easy to lose track of where you are when you are reading a number. For example, it is hard to differentiate between the 8th and 10th digit of this number:
101010101010101

Secondly, smaller bases will make longer numbers, that also compounds the problem mentioned above. That being said, I do not think that we will be using a different number system anytime soon. Also, even if we do, the most likely candidate is hexadecimal, not binary.

 

[nihilistic]

Also, regarding computing, there is a recent initiative to move beyond binary to either ternery or quaternary logic on slashdot:

SlashDot
Embedded.com Article

 

[Stile]

I would not be opposed to hexadecimal but you would have to rename all the numbers past say 12 for it to make sense for most people. So seventeen would be blahty-one and thirty-one would be blahty-blick and so on.

 

[h4ppy]

Well the Babalonians used base six. Thats why there are 360 degrees in a compass. There are a few more examples but most have been replaced by base 10.

 

[Ribannah]

The advantage of base 10 is that this gives two clearly different ways to make nice groups: in 2s or in 5s.

By the way, on 10 fingers we can easily count to 1023.

 

[Aphex_Twin]

It would be far too expensive to change the current numbering system. For instance, we are used to calculating in 10s. We also learn the multiplying tables in 10, to whick the whole modern math theory is founded on. Far too much trouble...

 

[nihilistic]

Originally posted by Aphex_Twin
It would be far too expensive to change the current numbering system. For instance, we are used to calculating in 10s. We also learn the multiplying tables in 10, to whick the whole modern math theory is founded on. Far too much trouble...

Multiplication tables can be easily altered. The theorems of mathematics do not change with respect to a change of the numbering system. Furthermore, most fields still researched today in mathematics don't really deal with numbers in a direct manner anyway.

But of course, the reason that it probably won't change is beacause that the general populace can't handle it. Changing the base system means a lot less than you may think to mathematicians.

 

[funxus]

Originally posted by Aphex_Twin
It would be far too expensive to change the current numbering system. For instance, we are used to calculating in 10s. We also learn the multiplying tables in 10, to whick the whole modern math theory is founded on. Far too much trouble...

The way to do it would be to start teaching people the new way, accepting both of them for a long period (30+ years) until most people can deal with the new system. But they'd have to put up a really good reason for people to bother.

EDIT: Hadn't read nihilistic's post until now.

 

[Maj]

"Changing the base system means a lot less than you may think to mathematicians."

Would it affect them in the same way changing from the Phoenician alphabet to Cyrillic would affect philosophers? In other words, you change the language and its symbols without impacting the ideas?

 

[Aphex_Twin]

We have been thought to think in 10s (including mathematicians). Changing the system would be like learning to add and multiply in anothe language. For me it's impossible to do it in English, but in comes naturally in Romanian. Your brain now has to call the "Language department" to decode the information, do the calculaitons, then translate back.