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Thread: Do do I say numbers in other bases?

  1. #1 Do do I say numbers in other bases? 
    Forum Junior c186282's Avatar
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    If I start counting in base 16 how should I say 10? Saying ten just feels wrong but saying sixteen also feels wrong. Is there a generalization for saying numbers in other bases?


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  3. #2  
    Universal Mind John Galt's Avatar
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    Shouldn't you just say 'A'?


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  4. #3 Re: Do do I say numbers in other bases? 
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    Quote Originally Posted by c186282
    If I start counting in base 16 how should I say 10? Saying ten just feels wrong but saying sixteen also feels wrong. Is there a generalization for saying numbers in other bases?
    The numbers are the same, no matter what base is used to represent them. Call them anything that you like, but twelve is still twelve, even if 12 is eighteen.
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  5. #4  
    Forum Junior c186282's Avatar
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    Quote Originally Posted by John Galt
    Shouldn't you just say 'A'?
    I'm happy to verbalize whatever symbols are used for the "ones" place but what generalized wording should I use for the "'s" place?
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  6. #5 Re: Do do I say numbers in other bases? 
    Forum Junior c186282's Avatar
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    Quote Originally Posted by DrRocket
    The numbers are the same, no matter what base is used to represent them. Call them anything that you like, but twelve is still twelve, even if 12 is eighteen.
    I realize that the concept of a number is septate from it representation in a given base. So are you suggesting I say twelve when I see c or when I see 12?

    The numbers 11-19 do not follow a good naming convention. (They should be something like onenty one, onenty two, etc like twenty one twenty two ..)

    So I'm looking for the "enty" and the "hundred" etc for base . So lets say these words are "hex" and "hexsquare" then the numbers would go like this:

    1 -> one
    f -> "f"
    10->"one hex"
    11->"one hex one"
    100->"one hexsquare"
    4e3 -> "four hexsquare e hex three"

    This is the type of thing that I'm looking for. Has anyone seen this type of thing before? If I just say twelve I also have to tell you the base. I think the base should be implied by the words used for the number. Of course the numbers from stand on there own
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  7. #6 Re: Do do I say numbers in other bases? 
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    Quote Originally Posted by c186282
    ... If I just say twelve I also have to tell you the base.
    No, you don't. "Twelve" is always twelve, and it has nothing to do with the base. It is only when you write it as 12 that you need to know the base. Twelve is also XII.

    I think the base should be implied by the words used for the number. Of course the numbers from stand on there own
    You are confusing language with mathematics. There is absolutely nothing that implies that words imply a base. Perhaps you could speak French when working in base 2 and German in base 16.

    The whole point is that the name of a number in any language has no necessary relationship to the number or to its representation in any particular base. Numerals and numbers are different things. Numerals are tied to representations and bases. Numbers have a life of their own.
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  8. #7 Re: How do I say numbers in other bases? 
    Forum Junior c186282's Avatar
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    Thank you for your time DrRocket but I think you have misunderstood the question.

    Do others have a comment? Do others think I'm off in left field?
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  9. #8  
    Universal Mind John Galt's Avatar
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    Quote Originally Posted by c186282
    Quote Originally Posted by John Galt
    Shouldn't you just say 'A'?
    I'm happy to verbalize whatever symbols are used for the "ones" place but what generalized wording should I use for the "'s" place?
    So you want to know how to say 3F, or B6, for example. I see the problem. When I wrote machine language routines for mini-computers we split the sixteen bit word into octal groupings. 1 010 110 101 011 001 became 126531, each numeral spoken separately. Perhaps you could do the same sort of thing: B6 is simply bee six.
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  10. #9 Re: Do do I say numbers in other bases? 
    Forum Ph.D. Leszek Luchowski's Avatar
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    Quote Originally Posted by DrRocket
    You are confusing language with mathematics. There is absolutely nothing that implies that words imply a base.
    Oh yes words do imply a base, albeit sometimes in an imprecise and ambiguouos manner. In most languages (European at least) the predominant base is 10, which is why it is so easy to read 3456 as [three thousand four hundred and fifty-six], with the thousands and hundreds explicitly named, and the tens reduced to "-ty".

    If you know how to count in French (the French of France as opposed to Belgium and Switzerland), you will have noticed a trace of base 20 in such words as quatrevingt - literally, "four twenties" or "four score", meaning 80, and even quatrevingt-treize, "four score and thirteen" (=93). Traces of the same can be found in old English text, as in wherever it was said that the span of human life is three score and ten years.

    Some more exotic languages regularly use base 5 or others, and people who speak those as their mother tongue have some difficulties learning the decimal system.

    Just as we find hexadecimal difficult to read out loud.
    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
    History teaches us that we don't learn from history.
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    Quote Originally Posted by John Galt
    [B6 is simply bee six.
    But he's not asking about B6, he's asking about 10(hex), which is 16(decimal). Or how would you pronounce 10 in this sentence: "There are 10 types of people, those who understand binary, and those who do not."
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  12. #11  
    Universal Mind John Galt's Avatar
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    Quote Originally Posted by Harold14370
    Quote Originally Posted by John Galt
    [B6 is simply bee six.
    But he's not asking about B6, he's asking about 10(hex), which is 16(decimal). Or how would you pronounce 10 in this sentence: "There are 10 types of people, those who understand binary, and those who do not."
    I was taught the count in hexidecimal was 1 2 3 4 5 6 7 8 9 A B C D E F. So 10(base10) in hex is A. So B6 is 11x16 + 6 = 176 +6 = 182 (base 10). What am I missing?
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    Quote Originally Posted by John Galt
    Quote Originally Posted by Harold14370
    Quote Originally Posted by John Galt
    [B6 is simply bee six.
    But he's not asking about B6, he's asking about 10(hex), which is 16(decimal). Or how would you pronounce 10 in this sentence: "There are 10 types of people, those who understand binary, and those who do not."
    I was taught the count in hexidecimal was 1 2 3 4 5 6 7 8 9 A B C D E F. So 10(base10) in hex is A. So B6 is 11x16 + 6 = 176 +6 = 182 (base 10). What am I missing?
    You are missing the number that comes after F.
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  14. #13  
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    10 (base 10) = A (hex)
    10 (hex) = 16 (base 10)
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  15. #14  
    Universal Mind John Galt's Avatar
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    Quote Originally Posted by Harold
    Quote Originally Posted by JohnGalt
    I was taught the count in hexidecimal was 1 2 3 4 5 6 7 8 9 A B C D E F. So 10(base10) in hex is A. So B6 is 11x16 + 6 = 176 +6 = 182 (base 10). What am I missing?
    You are missing the number that comes after F.
    I don't believe so. To expand on Jane's point and to write my own 'list' more accurately.
    Base ten ===> 0 1 2 3 4 5 6 7 8 9 There are ten numerals. We end on the 9th non zero numeral.

    Base sixteen ===> 0 1 2 3 4 5 6 7 8 9 A B C D E F There are sixteen numerals. We end on the fifteenth non zero numeral. The number after F is 10 (base sixteen).
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  16. #15  
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    Quote Originally Posted by John Galt
    The number after F is 10 (base sixteen).
    Okay. How do you pronounce that?
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  17. #16  
    Universal Mind John Galt's Avatar
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    Anyone for tenhex? :wink:
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  18. #17  
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    Quote Originally Posted by Harold14370
    Quote Originally Posted by John Galt
    The number after F is 10 (base sixteen).
    Okay. How do you pronounce that?
    You pronounce it "one zero hex" or "ten" "Hex". If in a crowd of assembly programmers "one zero" is enough. I guess you could get lazy and just say "one ooo" as in the letter O.

    Just like 8E7F would be said "eight E seven F". I use to write a ton of assembly language back in my younger days.
    Pleased to meet you. Hope you guess my name
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    Quote Originally Posted by (In)Sanity
    Just like 8E7F would be said "eight E seven F". I use to write a ton of assembly language back in my younger days.
    This is not how you would read a base ten number. So why is it aceptable for a base number. Also if you just read off a set of one digit numbers you would have to first tell me what base you are in. For example: AB (= 181 in base 10). It would have been much more clear if I could say "A" "word for a group of 17 things" B. (note AB was in base 17)
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  20. #19  
    Universal Mind John Galt's Avatar
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    Quote Originally Posted by c186282
    This is not how you would read a base ten number. So why is it aceptable for a base number.
    Simply because that is how it happened. That's two people who wrote assembly who apparently used the same system. It's anecdotal, but it's suggestive.
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  21. #20  
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    Quote Originally Posted by c186282
    Quote Originally Posted by (In)Sanity
    Just like 8E7F would be said "eight E seven F". I use to write a ton of assembly language back in my younger days.
    This is not how you would read a base ten number.
    Why not? If I have to look at a long base-ten number I would find it convenient to read out the numerals individually. Sometimes even not so long ones as well – for example, I often say “six six six” instead of “six hundred and sixty-six”.
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  22. #21  
    Forum Professor sunshinewarrior's Avatar
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    Quote Originally Posted by JaneBennet
    Why not? If I have to look at a long base-ten number I would find it convenient to read out the numerals individually. Sometimes even not so long ones as well – for example, I often say “six six six” instead of “six hundred and sixty-six”.


    "Woe to you o earth and sea for the Devil sends the beast with wrath..."

    Nice one, says the Iron Maiden fan (I prefer their more elliptical version to the full-on longer one from Revelation).

    Of course (more seriously) I suppose that one of the problems we have is that numbers are not alphabetic words, like most of the words we use in English, but logograms (or ideograms), in that they stand for ideas rather than sounds, so the pronunciation of them has to be by convention because the representation of the number does not give you a clue as to its sound. If you spell out the number (thereby making it effectively impossible to perform calculations using it) then this 'problem' goes away, but...
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  23. #22  
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    Quote Originally Posted by JaneBennet
    10 (base 10) = A (hex)
    10 (hex) = 16 (base 10)
    10 (base 10) = A (hex) = "ten"


    10 (hex) = 16 (base 10) = "sixteen"

    The whole point is that one simply must distinguish between the number and its representation in a selected base. The number is independent of the base.
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  24. #23  
    Forum Junior c186282's Avatar
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    Let me try and summarize a few things that have been said here and restate the question.

    I think we all agree that the concept of a number is independent of what base we are in and how we say it in our favorite language. The names of the numbers from are arbitrary. Also as one poster pointed out there are special words for numbers that are used sometimes like score, dozen etc.

    There are two ways of saying a number:
    1) Read out the digits one by one. However before this can work the two people need to agree on two things, The order the digits will be read (little ending or big ending) and the base. (The number 100101101001 could be in base 18 I just needed to use ones and zeros)

    2) Use our base ten words. Any number in any base can be said in our base ten words. "A" is ten. However this requires the user to convert the non-base 10 number to base ten to say it. (Without much work say: 3A4G8, it is in base 17) (If you do not think we use base ten words to say numbers try this: Write down the numbers 0 through say 20 in base 2 then say the numbers as you point to them and you will notice that your words do not reflect the change in the written symbols. However if you do the same with a list of base ten numbers you will notice that your words change in step with the changing symbols.)

    So the original question:
    Has anyone ever thought of or heard of how to say numbers in other bases? Again I have given my made up example using the root words "hex" and "hexsquare" for base 16.

    3C6 -> three hexsquare C hex 6

    This is similar to
    243 -> two hundred 4 "tee" 3

    PS Sorry about the typo in the subject of the original post.
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