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## #1 2006-02-03 07:40:30

DEALORNODEAL
Novice

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### Converting base ten to base four

Greetings,

I am able to convert base four to base ten, but I am having trouble trying to convert base ten to base four! I need to have these problems worked out so that I can see what it is I need to do to get the final answer.

WRITE THE FOLLOWING IN BASE FOUR:

2<ten> 8<ten> 21<ten>

## #2 2006-02-03 08:23:48

irspow
Power Member

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### Re: Converting base ten to base four

The easiest way that I have seen to convert a base ten (decimal) number to any other base is:

number/new base = new number + remainder (iteratively)

I'll use your numbers as an example;

2/4 = 0 + 2

2 base ten = 2 base four

8/4 = 2 + 0

2/4 = 0 + 2

8 base ten = 20 base four

21/4 = 5 + 1

5/4 = 1 + 1

1/4 = 0 + 1

21 base ten = 111 base four

Basically, your new number in the new base is just the reverse order of remainders from dividing your base ten number.  This system works for all conversions of base ten to any other base.

I hope that helped you.