Thread: position system

Hello I was thinking about the position systems the other day, and I started to wonder about something.

Binary, Hexdecimal and decimal are position system as I understand.
In decimal's case it means that you incrase the exponent the more you jump to the right.

But why bother nameing something positon system if there aint no other kind of systems.
So my question is: Are there any other kind of nummerical system then position system?

Some non-positional number systems:

1. Simple counting systems (tally marks, five bar gate, etc) are actually base 1 systems, but non-positional by definition.

2. Roman numerals (partially a tally system, as above).

3. Spoken numbers in modern languages. In English, "fifteen" is "five ten", meaning "15", yet "twenty-four" is "twenty four" meaning "24". In German, "dreiundzwanzig" is "three and two [times] ten", meaning "23". In French, "quatre-vingt-sept" is "four [times] twenty [and] seven", meaning "87". There's probably more languages like this.

Originally Posted by jrmonroe

Some non-positional number systems:

1. Simple counting systems (tally marks, five bar gate, etc) are actually base 1 systems, but non-positional by definition.

2. Roman numerals (partially a tally system, as above).

3. Spoken numbers in modern languages. In English, "fifteen" is "five ten", meaning "15", yet "twenty-four" is "twenty four" meaning "24". In German, "dreiundzwanzig" is "three and two [times] ten", meaning "23". In French, "quatre-vingt-sept" is "four [times] twenty [and] seven", meaning "87". There's probably more languages like this.

1. true, you mean like when counting up things like whats in a room: chair, book and bed?

2. roman numerals are very much positions system what I understand.
1V=4 but V1=6 how aint that a position system?

3."Dreiundzwanzig" would be like threeandtwoten, so if you swap em like twoandthreeten u get 32. And why is english different you have "fiveten"
but if you swap em it becomes ten five=50, and how is that not a position system?

Thanks for straightening me out.

1. Tallying, such as |, ||, |||, ||||, counting/showing fingers (which people still do in restaurants and bars), etc, it doesn't matter to which "side" (ie, position) you add the next "|". In base 1, 1^n = 1, so all the positions have the same value of 1.

2. Yes, in some ways, Roman numerals are very positional; yet "III" or "XXX" etc in Roman numerals is non-positional just like tallying above.

3. Well, I actually meant that the order of the words didn't reflect the order of the numbers themselves, but your right, my examples are positional. In English, "fifteen" and "fifty" both basically mean "five ten", but one means 5+10 (ie, 15) and the other means 5×10 (ie, 50), yet the parts of the words that mean "ten" are different enough to understand that one is added and the other is multiplied.

Generally, I think you were trying to say that the distinction of modern number systems being "positional" is pretty much passé, and you're right. Computers were probably the last nail in the coffin.

I think when most people say positional number system they mean something a little more specific than "the numbers depend on the position." See the Wiki article. By the more strict definition, roman numerals wouldn't be a positional system, even though the number represented does depend on the position.

Other than tally marks (and slightly more complex versions of tally marks, such as having a 1 mark, a 10 mark, etc.) I'm not sure how you'd have a counting system that doesn't depend on position in any way.

Originally Posted by MagiMaster

Other than tally marks (and slightly more complex versions of tally marks, such as having a 1 mark, a 10 mark, etc.) I'm not sure how you'd have a counting system that doesn't depend on position in any way.

Here's a webpage on positional and other number systems.

One way uses descriptors in lieu of positions. Traditional Chinese describes positions. 873 is written numerically as "eight hundred seven ten three". Although I have never seen it done, I suppose that 873 could be written as "three seven ten eight hundred". It would be like Latin in that it describes each element sufficiently that order/position often does not matter.