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The r ’s compliment 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 compliment will be equal to ( _____ )9.

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642?

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If base is r and you need to find r's complement then first find (r-1)'s complement.

Follow these steps:-

1. Subtract each digit of the given number from (r-1).

Here r=9 so r-1=8. Subtract 247 from 888 to get 641.

2. Then add 1 to it. 641+1=642

You can verify it for binary numbers, r=2. Say N=1011 then 1's complement is 0100. How we get it? By subtracting each digit drop from 1. So 1111-1011=0100. And add 1 so 2's complement becomes 0101.

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Brother when r is 2 then we subtract it from 1 because with base 2 highest possible sequence is 1, but for r= 9 the highest number will be (9^3)-1 so when we subtract given number with this we get 8s complement of the given number now to find 9s complement we will add one, so the for this answer for given question is:.

(247) = ((9^3) -1) -247 +1 = 482....!

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