More Converting Bases

Well, you've mastered the basics, so they say, but now I'm going to show you how to change a base 10 number to a base.  We will start with an example.  What is 17₁₀ in base 4?

Step 1) First what we do is divide the base 10 number by the number of the base you want to convert it to.
17 / 4 = 4 Remainder (R) 1.
Step 2) Make sure you have the remainder, and write it down. 1
Step 3) Now divide the quotient by the number of the base.
4 / 4 = 1 R 0
Step 4) Remember to make sure you have the remainder, even if it is 0.  Write this remainder TO THE LEFT of your other one.
01
Now, you're going to keep repeating the steps 3 and 4 until your quotient is less than the number of the base you were dividing by, and write that quotient to the left of all your remainders.  That is your number in the new base.
1 is smaller than 4, so we stop now.
101
So 17₁₀ = 101₄, tada!!!  We did it!

So there's one example, and it was pretty simple.  However, if we want to convert from one base that is not 10, to another that is not 10, it takes more time.  I don't know if there is a faster way, but I always go through base 10 (convert to base 10, then convert that to the other base).  Let's do one of those.  What is 95₆ in base 16?

95₆
5 => 0, 9 => 1
(5*6⁰) + (9*6¹) = 5 + 54 = 59₁₀
59₁₀ is what in base 16?
59 / 16 = 3 R11
Write remainder of 11 which is B, then 3 (because 3 < 16) to the left of it.
95₆ = 3B₁₆

Try some:
1. 1011011₂ to base 8
2. ABC₁₆ to base 2
3. 433₅ to base 3
Answers

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