This is HOW you do it. Ex. convert 125 from base 10(decimal) to base 2(binary):
125/2=62.5 if it leaves a fraction, then it is a 1. You write from R to L. Next:
62/2=31 if it leaves no fraction, then it is a o
31/2=15.5 it leaves a fraction, then it is a 1
15/2=7.5 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 1
7/2=3.5,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 1
3/2=1.5,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 1
The final 1 comes down as it is a,,,,,,,,,,,,,, 1
Then write it down from to top to bottom and going from right to left, thus:
1111101=125. Or, you can start from the bottom to the top and going from left to right, which is the same thing: 1111101=125. And that is it.
+129930 Here's an example....suppose we want to change 39 base 10 to a binary number....we divide repetitively as follows until we have a fraction < 1......
39 / 2 = 19 + remainder 1
19/2 = 9 + remainder 1
9/2 = 4 + reminader 1
4/2 = 2 + remainder 0
2/2 = 1 + remainder 0
1/2 = remainder 1
Now......write the remainders from bottom to top in order = 100111
This is the base 2 representation of 39.....
Proof
1*2^5 + 0 *2^4 + 0*2^3 + 1*2^2 + 1*2^1 + 1*2^0 =
32 + 0 + 0 + 4 + 2 + 1 =
32 + 4 + 2 + 1 =
39
