__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 17_{10} 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 17_{10} = 101_{4}, 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 95_{6} in base 16?

95_{6}

**5** => 0**, 9 **=> 1

(5*6^{0}) + (9*6^{1}) = 5 + 54 = 59_{10
}59_{10} 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.

95_{6} = 3B_{16}

Try some:

1. 1011011_{2} to base 8

2. ABC_{16} to base 2

3. 433_{5 }to base 3

Answers

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