Thread: 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)

Hey JojoZ.

Do you want to convert to base 10 and do it that way or do it natively in base 3?

can you show me in both ways

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).

okay this starting to make sense, can you teach me subtraction as well?

Give me some example numbers to work with.

21(base four) - 13(base four)

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.

why is 11-3=2?

Its in base 4, not base 10.

oh i get it now. Thanks so much for the help XD