# Complementary Number Systems

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If N = 670 in base 9 system. Then find the radix complement of N.

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180 in base 10 or 220 in base 9
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Radix = R's compliment = 9

8 8 8

-6 7 0

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2 1 8    in (R-1)'s compliment

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219 in (R)'s compliment but we can't represent 9 in base 9

So after 218 next number will come 220

So 218 + 1 = 220

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How 220 in base 9? @SHUBHAM SHASTRI

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i done like this 670 is in base 9 ..so converted into base 10 = 549 .

Now 9s complement of 549 = 9^3-549 = 180 in base 10 or 220 in base 9
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@SHUBHAM SHASTRI

Why are you doing like this...

Simply find the R-1 compliment

Why are you changing base and all its too time taking

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Ok. I figured this out.

N = (670) base 9.

now, 9’s complement = 8’s complement + 1
8's complement = 888-670 = 218
9's complement = 218+1 = 219, but we cannot represent 9 in base 9 number system. Now 9 in base 9 is 10.
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In 9's complement

largest number that can be displayed in 8's complement is 888

9's complement is (r-1)complement +1 = 889

now

889-670 = 219

9 can't be in base 9

so 220

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