self doubt

Question

How to do:(1000)base3 – (121)base3 without converting them to base 10 the final answer should be in base3

Answer 1

$(1000)_{3} -(0121)_{3}$. This would be much like subtraction in decimal system , only with one small change . While doing a borrow , instead of 10 , 3 will be borrowed.

The subtraction can be seen like :-

$(0223)_{3} - (0121)_{3}$[This is after doing the borrows.Kindly do it once , if not able to get i'll show the entire steps.]

Thus the difference will be $(0102)_{3} = 1*3^{2} + 2*3^{0} = 9+2 = (11)_{10}$.

Let's confirm this by converting this to decimal system.

$(1000)_{3} = (27)_{10}$

$(0121)_{3} = (16)_{10}$

$(27)_{10} - (16)_{10} = (11)_{10}$.

Answer 2

First you should know that , in any number system while doing subtraction, the borrow value will be of the value of radix of number system.This is the reason why we take 10 as borrow in decimal number system.Here, as the number system radix is 3.Hence the borrow value is 3. I think now you can do it easily!

                        https://drive.google.com/file/d/1I-cOyQzIGQNauHyy5rkBmAV4D3XzDMR1/view

Answer 3

While subtracting we take borrow 3.