The Gateway to Computer Science Excellence

0 votes

$(1000)_{3} -(0121)_{3}$. 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.

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

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

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

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.

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

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

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

0 votes

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

- All categories
- General Aptitude 1.9k
- Engineering Mathematics 7.5k
- Digital Logic 2.9k
- Programming and DS 4.9k
- Algorithms 4.4k
- Theory of Computation 6.2k
- Compiler Design 2.1k
- Databases 4.1k
- CO and Architecture 3.4k
- Computer Networks 4.2k
- Non GATE 1.4k
- Others 1.4k
- Admissions 595
- Exam Queries 573
- Tier 1 Placement Questions 23
- Job Queries 72
- Projects 18

50,737 questions

57,291 answers

198,210 comments

104,898 users