
 mikau
 Super Member
those who speak binary..
So the other night I was thinking, why is it so much easier for me to think in base 10 than in base 2? Is it just because I'm always translating base 10 so I feel more comfortable? If we rewrote history such that we always used based 2, all of us should be perfectly comfortable with seeing a number like 10010100 and instantly get a sense of the size of the number. So why don't I? Is it just unfamiliarity? Or is there some other difference that makes it seem awkward?
The only answer I came up with is I know of no way to actually verbalize a number in binary. In base 10 we have special names for the first 3 powers of 10 (one, ten, hundred) and then a new name for every 3rd power of 10 from then on (thousands, millions, billions, etc) which we combine with the first three terms to express every power of 10.
So if we'd like to verbalize a binary number, shouldn't we have special names for say, 1, 2, 4, and then special names for 2^3, 2^6, 2^9, ... etc? rather than calling them the '128's' column, which is describing the number in base 10?
So let me try giving intuitive names to these values: 1: one 2: pair 4: quad
and some arbitrarily selected names to the following: 8: spider 64: chess 512: hawk
I chose Hawk for Tony Hawk, world renowned skateboarder born on 5/12. (I'm open for better suggestions! )
Anyway, using the terms defined thus far, we can take any number between 0 and 2^10  1, (any 9 digit binary number) and read it! like we do with base 10.
examples: 1001 add commas after every third digit like we do in base 10: 1,001
we now have 'one spider, one.
or say, 111,001
can be read: one quad pair one spider, one.
lastly, take the biggest number available:
111,111,111
this is:
one quad pair one hawk, one quad pair one spider, one quad pair one.
The only trouble I see, is that you need a lot more names just to cover every number between 1 and a million, than you do in base 10. In base ten we only need 2, in base two, we need 7, for the following values:
8 64 512 4096 32768 262144 2097152
Still, it can be fun to make up your own names for these numbers. I tried to use names that were in some way related, so they were easier to remember, but that pretty much stopped working after 64. But you could use some other sort of naming convention. You can also rename 1, 2, and 4.
What names would you give these numbers?
Last edited by mikau (20080914 08:17:37)
A logarithm is just a misspelled algorithm.
 Chewy
 Full Member
Re: those who speak binary..
Focusing on "ary", you could use:
8 = octary (from Latin, "octava", which in music gets written sometimes as "8va" 16 = hecktary (inspired from but NOT related to the term "hexadecimal" 32 = aviary 64 = topiary 128 = mercenary.... etc LOL
negatives would of course start with :
2 = contrary 4 = cemetary 8 = (d)ocumentary (playing off the "oct" for 8 above
A fixed constant would be:
k= stationary
Ok, not funny any more, if it was at all. I had fun anyway
Last edited by Chewy (20080918 08:32:26)
 Ricky
 Moderator
Re: those who speak binary..
Why not just keep it the same?
10010 is ten thousand and ten.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
 Chewy
 Full Member
Re: those who speak binary..
But then what would happen when you get to 10012 ? In binary that is : 10011100011100
 Chewy
 Full Member
Re: those who speak binary..
and 10010 is 18
Re: those who speak binary..
The reason you wouldn't use decimal names is it stops you being able to decipher the size of the number, because you hear it said as though it were decimal, so you instantly think of it as being decimal and think of a massive number.
The Beginning Of All Things To End. The End Of All Things To Come.
 MathsIsFun
 Administrator
Re: those who speak binary..
This is fun
Ummm... do you need to say "one" quad ... just quad is enough (it is either there or not!)
So:
111,111,111: quadpairone hawk, quadpairone spider, quadpairone.
Plus, it may be better to have groups of 4 so we have:
1: one 2: pair 4: quad 8: oct
1,1111,1111: one hawk, octquadpairone spider, octquadpairone.
That way we need less names.
And, at the risk of being boring it may be better to choose a combination name, like "bibin" "tribin", "quadbin" for each group of 4
1,1111,1111: one tribin, octquadpairone bibin, octquadpairone.
1,1010,0000,1100: one quadbin, octpair tribin, octquad.
But I am not happy with "quadbin" as it would get confused with "quad".
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman
 mikau
 Super Member
Re: those who speak binary..
Ricky wrote:Why not just keep it the same?
10010 is ten thousand and ten.
exactly as luca said! The whole point of this discussion is to escape the habitual base 10 mindset. If we start using base 10 names to describe them, that just defeats the point of this whole discussion. (in my oppinion? )
I agree with you, mathsisfun, I noticed that. I was just doing that so it sounded exactly like how we verbalize numbers in base 10. But yeah, thats easier and actually less confusing. So, better in every way.
LOL! I love your 'ary' theme idea, chewy! awesome! However, you need to be thinking of only names for the values 2^(3m) with m an integer greater or equal to 1.
another thing worth noting, is that, like i said, in base 10 we always use something between 1 and 999 before one of the big names, and here we're using something between 1 and 2^31 before each big name, (1 to 7)
groups of 7 or less are much easier to visualize in your head than groups of say, 788. I mean i can easily picture 7 cookies in my head but 788 is just hard.
Last edited by mikau (20080919 14:50:47)
A logarithm is just a misspelled algorithm.
 MathsIsFun
 Administrator
Re: those who speak binary..
The solution to my quad/quadbin quandary is quabin.
Each group could have these names: (none), bibin, tribin, quabin, pebin, hebin, sebin, ocbin, nobin, debin
So, 2^16 (1,0000,0000,0000,0000) would be one pebin. You could figure it out by remembering that 2^0 is the units place, so 2^16 must be the 17th place, and hence the start of the 5th group "pebin". And 2^32 would be one nobin.
If you had to use binary A LOT this may even be useful
And you could make life easier by calling "1111" a "full"
So 2^16  1 (1111,1111,1111,1111) would be "full quabin, full tribin, full bibin, full"
Yeehaa!
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman
 mikau
 Super Member
Re: those who speak binary..
but ONLY useful if we spread the word so everyone understands it!
Everybody, TELL YOUR FRIENDS!
A logarithm is just a misspelled algorithm.
 LQ
 Real Member
Re: those who speak binary..
Myself is my best friend; I have one
I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...
Re: those who speak binary..
Having spent 25yrs in the computer and telecoms industry, I'd say that we don't use binary often, but instead either octal or hex. These are used more in examining file dumps and errors closeup to the computer hardware, especially C or assembler. At this level its seldom needed to get an understanding of the relative size of the value.
Hex needs letters A to F to represent the values 10 to 15. Octal just uses 0 to 7. But you knew this already. All Octal numbers can be [mis] pronounced as if they were decimal, so 376[octal] is often said threesevensix. Hex numbers can be more awkward, and 2B53 would commonly be pronounced twobeefiftythree. No, noone I worked with ever cared about the "wrongness" of what they said.
Re: those who speak binary..
If you construct a way to verbalize binary in just the right way it can also double as a 'native hexadecimal' verbalization too.
For fun you can play around with this online tool: http://www.castedo.com/binspeak/ and see how speaking binary with single sounds instead of words representing powers of 2 could work. You can even input your own choice in sounds for representing the various required powers of 2.
For instance, with the sound choices I currently like, 1 1010 0000 1100 (or 0x1A0C in hex) would be verbalized: "ika usuma uis" ("eekah oosoomah ooees")
ika is 0x10 ("hexadecimal ten") usu is 0xA ma is 0x100 ("hexadecimal hundred") uis is 0xC
Input your own numbers and verbalization and see what they convert too on the fly.
