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[Pickerel]

Base 12 is still hard to work with as a human.  Base 8 and 16 are good for computers because it makes good use of their binary storage (or something like that, I am not well versed herein) but as a human, I like to be able to multiply and divide things easily.

Example: lets say base 12 sconds, base 12 minutes, somehow.  I say 34 minutes, how many seconds is it.  34 * 12 is not something I can do in my head.  If under a base 10 time system though, I say 34 minutes, I say 3400 seconds, 0.34 hours, 0.034 days.  Try 1342.56 minutes.  I can say 1.34256 days, or 13.4256 hours, or 134256 seconds.  Base 12 would be... egads, I am still not going to try.  And I don't feel like trying in the 60:60:24 system either ^.^

Another point in favor: once you get into decimals of seconds, you use a base 10 system, because if you had to use fractions to do the math in our base 60, 60, 24 system, or even base 12, it would be really difficult.

[ March 12, 2008: Message edited by: Pickerel ]

[Puzzlemaker]

Did someone say... Celsius?

0  - freezing
10 - cold
20 - cool
30 - warm
40 - hot

There you go.  Freezing, Cold, Cool, Warm, Hot, starting at 0.  Celsius is sooooo much easier then Fahrenheit.  

AS FOR BINARY, Another lowdown!

Binary is base 2.  We normally use base 10.

00, 01, 02, 03, 04, 05, 06, 07, 08, 09
10, 11, 12, 13, 14, 15, 16, 17, 18, 19

That's base 10.  Base two is...

00, 01
10, 11

There you go.  Now, binary is stored in Bytes.  Each Bytes has 8 bits.  In laymens terms, the computer stored stuff in chunks of 8 digits.

00000000

So, how can you easily see what is being shown?

01001011

It's not easy to look at a huge stream of 1's and 0's and figure stuff out.  So, it's split into two four-digit groups, called Nybbles.  Nybbles, Bytes, get it?  haha?

Anyway, split into two different groups of 4 digits.

0000
0000

Each group of four digits can count up to a max of 16.

0000 - 0
0001 - 1
0010 - 2
0011 - 3
0100 - 4
0101 - 5
0110 - 6
0111 - 7
1000 - 8
1001 - 9
1010 - 10
1011 - 11
1100 - 12
1101 - 13
1110 - 14
1111 - 15

Since we started at 0, thats 16 different possible numbers.  Well, heck, lets just count in base 16!  Base 16 is:

00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 0A, 0B, 0C, 0D, 0E, 0F
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F

As you can see, the extra numbers are replaced with letters.  Now we can represent bytes with two hex digits, like so.

FF = 1111, 1111
F0 = 1111, 0000

etc, etc.  

NOW YOU KNOW!

(The same applies for base 8, but that's for 3 bits, 000)

[Jamini]

Binary counting easily allows one to count to 1023, additionally it's excessivly easy to work arithmatic on when all you have are 1 and 0 for digits. The only reason that many computer languages use Hexadecimal for microprograms and above is  because computers often deal with far more than digits and need to perform operations on several high-order binary numbers. Hexadecimal can use a single digit to display four binary digits, making it idea for expressing notation.

Also, with a little practice anyone can learn their base-16 tables. Just remeber where your median values are. I mean if you remember that 04H*08H= 20H than it's easy to inferance that 04H*09H=24H. (1*9=9. 2*9=12. 3*9=1A, 4*9=24)

[BurnedToast]

quote:Originally posted by Puzzlemaker:
<STRONG>Did someone say... Celsius?

0  - freezing
10 - cold
20 - cool
30 - warm
40 - hot

There you go.  Freezing, Cold, Cool, Warm, Hot, starting at 0.  Celsius is sooooo much easier then Fahrenheit.  
</STRONG>

You must live somewhere really warm to consider 68ºF cool and 86ºF merely warm.

[Puzzlemaker]

quote:Originally posted by BurnedToast:
<STRONG>

You must live somewhere really warm to consider 68ºF cool and 86ºF merely warm.</STRONG>

Ah, crap, my bad.  I have a 25C in there usually that I like to use in my internal calculations, and it threw me off.

0 - freezing
10 - cold
20 - normal
30 - hot
100 - boiling

[Janne Joensuu]

quote:Originally posted by Pickerel:
<STRONG>Example: lets say base 12 sconds, base 12 minutes, somehow.  I say 34 minutes, how many seconds is it.  34 * 12 is not something I can do in my head.  If under a base 10 time system though, I say 34 minutes, I say 3400 seconds, 0.34 hours, 0.034 days.  Try 1342.56 minutes.  I can say 1.34256 days, or 13.4256 hours, or 134256 seconds.  Base 12 would be... egads, I am still not going to try.  And I don't feel like trying in the 60:60:24 system either ^.^</STRONG>

Under base 12, 34 would be written 30. 3*12 + 0. 12-base 17 would be 12-base 15 (1*12 + 5). 10-base 10 and 11 would be marked by a single character, likely A and B. 6 + A = 14 (10-base: 6+10=12+4), 20 - 2 = 1A (24-2=12+10), 14+8 = 20 (12+4+8=24) etc. 20/2 = 10, 20/3 is 8, 20/4 = 6, etc.

10 is 12, 100 is 144, 1000 is 1728. 20736  12^5--248832, 12^6--2985984, 12^7=35831808

As far as your examples go...

First, how many seconds (12 seconds in a minute) are in 34 minutes? In base 12, 12 equals 10 and 34 equals 2*12+10 or 2A.
1 minute has 10 seconds. How many seconds are there in 2A minutes? 2A*10 = 2A0.

2A0 is 2*144 + 10*12 + 0, or 408.

Let's see if that's right: calculator says 12*34 is... 408! Conversions back into ten-base are tricky, but calculating in 12-base really is that easy.

Second, calculating 3400 in 10-base:
3400 - 1*1728 = 1672
1672 - 11*144 = 88
88 - 7*12 = 4
4 - 4*1 = 0

It's 1A74 in 12-base. Going through the above calculation in base-12 is easy:

1A74 - 1000 = A74
A74 - A00 = 74
74 - 70 = 4
4 - 4 = 0

10-base 0.34 would be... slightly over 12-base 0.4 which would be an exact 1/3.
Base-12 0.2 is 1/6, 0.3 is 1/4, 0.4 is 1/3 and 0.6 is 1/2.

I won't bother calculating Pi.
I'm not even sure why I did this, but you didn't even think your examples through. Base 12 will have problems with numbers that are easy in base 10 (like 10, 100, 1000) and with dividing by 5, but base 10 has problems with numbers that are easy in base 12 (like 12, 144, 1728) and with dividing by 3, 4 or 6.

[Helmaroc]

No wonder Fenrir left, this much...nubmers...would scare anyone out of their wits.

[Kagus]

Show someone how proficient you are with binary numbers by counting to four on one hand, using the binary system.

Only someone who's done this will know what I'm talking about.

[Kashyyk]

quote: Only someone who's done this will know what I'm talking about.

 

[Alfador]

quote:Originally posted by Kagus:
<STRONG>Show someone how proficient you are with binary numbers by counting to four on one hand, using the binary system.

Only someone who's done this will know what I'm talking about.</STRONG>

Yeah, I got in trouble in elementary school for binary counting to 132 in front of a teacher. That was actually how I found out that hand gestures can make people angry. My mom didn't punish me because I had no idea what it was, then she taught me so I would know not to do it again. Now I avoid counting to 132 at people unless I intend to be rude to them.  

[n9103]

lol, double birds.... best way to avoid offense when binary counting is to have them flat on a surface/parallel with the ground... then it's usually no more offensive than people who point at things with their middle fingers (and yes, there are people so uptight even that's offensive)