Bases (Binary,etc.)

MathIsGreat · P versus NP Offline Joined: 20 Jan 2008 Posts: 32

Again, I think this goes here...

Does anyone have an easy way to convert numbers from base 10 to whatever base?
Or vice versa?

Thanks!

**Posted:** Tue Nov 03, 2009 8:03 pm

AndrewTom

Hi MathIsGreat.

How about here: http://en.wikipedia.org/wiki/Positional_notation

Hope this helps.

**Posted:** Tue Nov 03, 2009 11:20 pm

MathIsGreat · P versus NP Offline Joined: 20 Jan 2008 Posts: 32

thanks!
However, I was looking for a more basic explanation...

**Posted:** Wed Nov 04, 2009 8:45 pm

darkmage2009

I assume you already know what a number in base $n$ means. (For example, $(123)_4$ equals $1\cdot4^2+2\cdot4^1+3\cdot4^0=27_{10}$ )
Converting from base 10 to another base is not too difficult, since it only involves division that you are familiar with. For example, let's try converting $(1000)_{10}$ into base 2. (Note, in the calculations below, I will omit the subscript for base 10 because we are converting from base 10).
$1000/2=500+0$
$500/2=250+0$
$250/2=125+0$
$125/2=62+1$
$62/2=31+0$
$31/2=15+1$
$15/2=7+1$
$7/2=3+1$
$3/2=1+1$
$1/2=0+1$
We stop here because furthering this process will just create more zeroes. If you think about it, the last remainder has gone through the most divisions by 2, so it's the highest power of 2, so we take the remainders in reverse order. Therefore, $1000=(1111101000)_2$ .

**Posted:** Thu Nov 05, 2009 8:03 am

_________________
1+1=2 in base 10, and 1+1=10 in base 2. Coincidence? I think not!

AndrewTom

Hi MathIsGreat.

Is the following site any better?

http://www.mathpath.org/concepts/Num/conv.htm

**Posted:** Thu Nov 05, 2009 9:43 am

MathIsGreat · P versus NP Offline Joined: 20 Jan 2008 Posts: 32

thanks guys!

**Posted:** Thu Nov 05, 2009 8:35 pm