How do you say '10' when it's binary?

Factual Questions
61

People here are confusing “digits” with “numbers.” Numbers are those things that have quantity, regardless of which base is being used. Digits are the representations we use to express numbers.

In our base 10 system, we have, not surprisingly, ten digits we use (maybe it is surprisingly, since the Romans had the same system, but used a wholly different set of “digits”): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

The names for these are zero, one, two, three, four, five, six, seven, eight, nine. Not shockingly, they correspond to their numerical counterparts. That is, the name for the digit is the name we use for the number it represents.

“Ten” is not a digit. It’s a number. It is ((((((((1 + 1) + 1) + 1) + 1) + 1) + 1 ) + 1) + 1) + 1 of a thing. We represent it in our system with the digits “one zero”, written 10. We then say “ten” for that representation.

When you are in base eight, 10 no longer represents “ten.” Ten, you will recall, is a number. 10[sub]8[/sub] represents “eight.” 11[sub]8[/sub] represents “nine.” 12[sub]8[/sub] represents “ten.” If you say “ten base 8” you are meaning 12[sub]8[/sub]. You cannot possibly mean 10[sub]8[/sub], because that representation is not the same as the number 10.

62

Hear, hear [although your very last bit could’ve been phrased better; I’d’ve said “not the same as the number ten” to stave off ambiguity (not actually really present, though, since we all agree that digit-strings are normally interpreted as decimal representations)].

63

My HS Algebra teacher told us that the Romans had no way of expressing zero. If that’s true, did they actually have an incomplete form of base 10?

64

The Romans didn’t use base 10, in the modern sense. They used… Roman numerals.

(Well, of course, later on Romans adopted Hindu-Arabic numerals and positional notation, just like most of the world.)

65

So I went (where else?) to Wikipedia:

In general, the number zero did not have its own Roman numeral, but a primitive form (nulla) was known by medieval computists (responsible for calculating the date of Easter). They included zero (via the Latin word nulla meaning “none”) as one of nineteen epacts, or the age of the moon on March 22. The first three epacts were nullae, xi, and xxii (written in minuscule or lower case). The first known computist to use zero was Dionysius Exiguus in 525. Only one instance of a Roman numeral for zero is known. About 725, Bede or one of his colleagues used the letter N, the initial of nullae, in a table of epacts, all written in Roman numerals.

It’s interesting to note that they had fractions as well, using dots. They were based on twelfths, however and used dots and such.

*1/1728 siliqua, siliquae, represented by a symbol resembling closing guillemets » *

66

What am I, invisible?

67

Sure they did, how do you think they counted to a hundred? Just like us they had a ten-based name for 20, 30, 40, 50, etc. and put the numbers 1-9 next to it. I’d say that’s a clear indicator of a decimal counting system. Just because they didn’t use Arabic numerals doesn’t mean it wasn’t base 10.

68

As I said before, just because a language uses a counting system clearly grounded in 10 doesn’t mean it’s a base 10 positional system, in the relevant sense of this thread. Where’s the natural progression between the names for one, ten, hundred, and thousand in English, for example?

69

Well they omitted zero, and as far as I could see in that wiki article, there wasn’t a mention of negative numbers.

Though the Romans used a decimal system for whole numbers, reflecting how they counted in Latin, they used a duodecimal system for fractions, because the divisibility of twelve (12 = 3×2×2) makes it easier to handle the common fractions of 1/3 and 1/4 than does a system based on ten (10 = 2×5).

So they had the counting numbers but not zero, really. They didn’t have decimals; they had “duodecimals,” still base 10. So they were base ten, but didn’t use it to describe as many things as we do?

Pythagorean theorem - Wikipedia says:

However, when authors such as Plutarch and Cicero attributed the theorem to Pythagoras, they did so in a way which suggests that the attribution was widely known and undoubted.

Cicero died in 43BC, so the Romans had it at least by then. I wonder how the Romans represented square roots, of if they just relied on natural triples for all their building.

70

You are assuming that your are basically ( :cool: ) working in decimal here. There are a lot of situations in which the decimal value of the bit string is totally irrelevant - for instance when you are working with fields of a word. In that case, saying say 12[sub]16[/sub] means that the first byte has a 1 and the second has a two. You don’t care at all that this happens to be decimal 18, since each byte might represent a field in a microinstruction or a register or something like that.

Each collection of bits can be represented by a decimal number, but often that isn’t very helpful. In fact, on my whiteboard right now I’ve got I’ve got a sketch of the 64 bit device id register of a processor, with an 800 bunch of blanks 1fffff in it. I assure you I don’t care what the numeric value of this thing is.

71

100[sub]8[/sub] would be said 64 if you were going by that method (10[sub]8[/sub] * 10[sub]8[/sub] = 100[sub]8[/sub] = 8 * 8 = 64).

As for the posts right above mine on this page (specifically DSYoung’s), it doesn’t really matter what the decimal representation is. Ten is a number and a string of digits, and when I’m reading off litanies of numbers for people to copy down it’s a lot less time consuming to say one-thousand-base-eight than one-zero-zero-zero-base-eight (or octal), everyone knows what I mean (hopefully). It’s also a lot easier for everyone to know 1000 is that set of digits than having to repeat after “what was digit four again? I missed it.”)

Overall it really seems to be a preference thing, depending on the definition of “ten” you’re using (and we’ve seen both definitions technically exist from the dictionary cite earlier), ten-base-eight and one-zero-octal, and “eight” are the same thing, though when talking to others the last one is pretty much out of the question, especially if this decimal representation is irrelevant (on preview, like Voyager said).

Also, link to the Tom Lehrer piece mentioned, because it’s awesome (and shows how different ways to say it sounds at least iirc he manages to say both one-two and <number>-base-eight in the same piece):

ETA: Nevermind he says <digit>-<digit>-base-eight the whole time, but I stand by my feelings!

72

Which dictionary cite? I must’ve missed it.

73

CTRL+f’ing I misread your post last page the first time around thinking you said you FOUND one… carry on. Sorry about that, my mistake.

(And you were right by the way, the primary definition is “the number of nine plus one”)

74

Jragon, the fact that many people who work extensively in a different base “mis-use” the words for our numbers to represent the written digits they see doesn’t make it “correct.” And, I doubt that there is consensus even among those who use base-8 or base-16 regularly as to what to say.

As with all communication, if saying “ten base 8” communicates the number 10[sub]8[/sub], which is really the number eight, then use it. But hopefully, you would understand why it’s not “correct” to do so. :slight_smile:

75

Items related to the concept of zero:

http://www.flickr.com/photos/24524964@N08/2316487968/

76

Meh. “There are 2 types of people in the world: those who understand hexadecimal and those who don’t” is funnier anyway…

77

I have read quickly all the previous replies and although I might have missed something, I don’t think anyone has answered the original question. Which does not surprise me because I asked the same question about a year ago and in spite of many replies never received an answer either. It was as if people did not understand my original question. Let me try again.

Suppose I give you an apple, and then I give you another apple, and then I give you another apple, and then I give you another apple,and then I give you another apple. I then ask you to write down how many apples I have given you using base 10. You would write “5.” If I then asked you how “5” is pronounced, you would say “five.” Now if I do the same to someone using base 2, he would write “101.” If I asked him how it is pronounced, what would he say? One oh one? One hundred and one? Five? Something else?

78

My vote is “five”, the quantity is the same, the digits don’t change that.

If you had “one hundred thirty five” apples and were asked how many he had, you wouldn’t say “one, three, five”, you’d use the words.

The words themselves, I argue, have no numeric base, only the digits that represent those words have a base. If you had to write that quantity on a piece of paper in order to answer the question (and use digits, not words), then the base becomes important.

79

What about this? You hand me apples and I write down how many there are. You give me five apples. I write down V. How is that pronounced? It’s pronounced “five.” You give me a hundred and thirty seven apples, I write down CXXXVII. You point that out and say “what number is that?” I’d be daft to say “it’s pronounced see eks eks eks vee eye eye.” It’s prnounced “one hundred and thirty seven.” What about the word “the”? If someone points it out and says “how do you say that word” you don’t respond “tee aitch aieee!”

This is all very sad because it means there isn’t any way to tell the “joke” to your friends. You have to very cleverly print it on a t-shirt and force them to wear it. This, and flossing, are how you know that God has abandoned you.

80

Really? I’d pronounce that “quinque”.

In an amusing coincidence, I was coming back from lunch the other day with a particularly nerdy professor, and he told this exact joke (though the rest of us were of course familiar with it already). He pronounced it “ten”.

On another side note, I’ve never told a joke in base baker’s-dozen (calling that number by the name “thirteen” reflects an inherent decimicentricism). But I have actually done some work in base eleven, for a programming project I worked on in my free time. It turns out to crop up naturally in analysis of the Connect-4 game.