Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

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 (2008-09-13 10:17:37)*

A logarithm is just a misspelled algorithm.

Offline

**Chewy****Member**- Registered: 2008-08-07
- Posts: 67

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 (2008-09-17 10:32:26)*

Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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..."

Offline

**Chewy****Member**- Registered: 2008-08-07
- Posts: 67

But then what would happen when you get to 10012 ? In binary that is : 10011100011100

Offline

**Chewy****Member**- Registered: 2008-08-07
- Posts: 67

and 10010 is 18

Offline

**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

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.

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,529

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: quad-pair-one hawk, quad-pair-one spider, quad-pair-one.

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, oct-quad-pair-one spider, oct-quad-pair-one.

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, oct-quad-pair-one bibin, oct-quad-pair-one.

1,1010,0000,1100: one quadbin, oct-pair tribin, oct-quad.

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

Offline

**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

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 2^3-1 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 (2008-09-18 16:50:47)*

A logarithm is just a misspelled algorithm.

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,529

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

Offline

**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

but ONLY useful if we spread the word so everyone understands it!

Everybody, TELL YOUR FRIENDS!

A logarithm is just a misspelled algorithm.

Offline

**LQ****Real Member**- Registered: 2006-12-04
- Posts: 1,281

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...

Offline

**random_fruit****Member**- Registered: 2008-12-25
- Posts: 39

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 close-up 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 three-seven-six. Hex numbers can be more awkward, and 2B53 would commonly be pronounced two-bee-fifty-three. No, no-one I worked with ever cared about the "wrongness" of what they said.

Offline

**castedo****Member**- Registered: 2009-12-16
- Posts: 1

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.

Offline

Pages: **1**