3 votes 3 votes The r ’s complement of an n-digit decimal number N in base r is defined for all values of N except for N = 0. If the given number is (247)9, then its 9’s complement will be equal to ( _____ )9. Digital Logic digital-logic number system + – Lakshman Bhaiya asked Jan 5, 2018 Lakshman Bhaiya 1.6k views answer comment Share Follow See all 12 Comments See all 12 12 Comments reply Pawan Kumar 2 commented Jan 5, 2018 i reshown by Pawan Kumar 2 Jan 6, 2018 reply Follow Share 642 ? 1 votes 1 votes Ashwin Kulkarni commented Jan 5, 2018 reply Follow Share Answer should be $(482)_9$ Its not base 10 number its base 9 number hence b’s compliment in base B = $b^n - x$ $729_9 - 247_9= 482_9$ 1 votes 1 votes Balaji Jegan commented Jan 5, 2018 reply Follow Share How to find the 8's compliment for this number?? 0 votes 0 votes Ashwin Kulkarni commented Jan 5, 2018 reply Follow Share if number is base 9, then 8th compliment will be (b-1)'s compliment Then you can find it out by $(b^n - 1) - x$ 2 votes 2 votes joshi_nitish commented Jan 6, 2018 reply Follow Share @Ashwin, you are not doing correct, firstly, $729_9-247_9=482_9$ is (729)9 possible in base 9 ? you can find solution of above qsn like this, (b-1)th comlement = 8th complement = $888_9-247_9=641_9$ now bth complement = 9th complement = $641_9+1_9=642_9$ 1 votes 1 votes Lakshman Bhaiya commented Jan 6, 2018 reply Follow Share my answer is 641 why? 642 0 votes 0 votes Ajay Jadhav commented Jan 6, 2018 reply Follow Share how digit 9 is present in729 which has base 9? 1 votes 1 votes vamp_vaibhav commented Jan 6, 2018 reply Follow Share Answer given by Joshi nitish is absolutely correct.. 0 votes 0 votes Lakshman Bhaiya commented Jan 6, 2018 reply Follow Share not possible 729 in base 9 0 votes 0 votes Ashwin Kulkarni commented Jan 6, 2018 reply Follow Share My bad ! :(( yes you are correct @nitish 0 votes 0 votes Pawan Kumar 2 commented Jan 6, 2018 reply Follow Share for such que , for a given base B, if B's compliment is asked , then subtract the LSB with B and rest upto MSB , with B-1 eg here (247)9, subtract the LSB with 9 , and rest upto MSB with 8..... But if the LSB is 0 or if 0 is encountered from LSB to a given point going from left to right, keep writing 0 as it,subract the first encountered with B , and rest upto MSB with B-1. eg if 9's compliment of (246000)9 was asked , ans would have been (643000)9 Given is for 10's compliment but general can be found with any base.. Hope this helps a little 0 votes 0 votes Vipin Rai commented Apr 28, 2018 reply Follow Share In base 9 the digit range will be from 0 to 8 , so if we make all 3 digits as 8 then it will be the maximum number. so 888 - 247 = 641 which will be the 8's compliment. For 9's compliment add 1 = 641 + 1 = 642 All are in base 9 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes The r’s complement of an n‐digit number = $r^{n} - N$ for $N \neq 0$ here we need to find 9's complement of $\left ( 247 \right )_{9}$ $\Rightarrow 9^{3} - 247$ $\Rightarrow 1000 - 247$ $\Rightarrow 642$ Note : All above calculation are in base 9 Mk Utkarsh answered Apr 22, 2018 Mk Utkarsh comment Share Follow See all 0 reply Please log in or register to add a comment.