# Base three division

• Feb 11th 2013, 09:20 PM
JojoZ
Base three division
I need help with division in base three;
Find the quotient for 222(base three) / 22(base three)
it would be helpful if you can explain step by step

I also need help with subtraction in different bases beside base 10. For example 21(base four) - 13(base four)
• Feb 11th 2013, 09:23 PM
chiro
Re: Base three division
Hey JojoZ.

Do you want to convert to base 10 and do it that way or do it natively in base 3?
• Feb 11th 2013, 09:42 PM
JojoZ
Re: Base three division
can you show me in both ways
• Feb 11th 2013, 09:57 PM
chiro
Re: Base three division
In base 10 we convert both by using

2*3^2 + 2*3^1 + 2*3^0 = 18 + 6 + 2 = 26 in Base 10
2*3^1 + 2*3^0 = 6 + 2 = 8.

26/8 = 3 remainder 2 Which gives a quotient of 3 and in base 3 that is 10_(base3)

To do it in base 3 natively we use the long division algorithm

222
)-------
22

22 goes into 222 10 times (remember 10 is 3 not 10 in base 10)
22*10 = 220
222-220 = 2

So 222_(base 3) = 22_(base3) * 10_(base3) + 2_(base3).
• Feb 11th 2013, 10:04 PM
JojoZ
Re: Base three division
okay this starting to make sense, can you teach me subtraction as well?
• Feb 11th 2013, 10:20 PM
chiro
Re: Base three division
Give me some example numbers to work with.
• Feb 12th 2013, 09:21 AM
JojoZ
Re: Base three division
21(base four) - 13(base four)
• Feb 12th 2013, 04:04 PM
chiro
Re: Base three division
21-13 (Base four).

1 is less than 3 so we cross out 2 replace with 1 and we get 11-3=2. Then we do 1-1 (remember we crossed out 1 in 2nd digit) = 0 so 21-13 = 2(base4).

Confirming in base 10, we get 21 = 2*4^1 + 1*4^0 = 9 and 13 = 1*4^1 + 3*4^0 = 7 and 9-7 = 2 as expected.
• Feb 12th 2013, 04:58 PM
JojoZ
Re: Base three division
why is 11-3=2?
• Feb 12th 2013, 06:30 PM
chiro
Re: Base three division
Its in base 4, not base 10.
• Feb 12th 2013, 08:53 PM
JojoZ
Re: Base three division
oh i get it now. Thanks so much for the help XD