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# 9s complement and 10s complement | Subtraction

Before knowing about 9's complement and 10's complement we should know why they are used and why their concept came into existence. The complements are used to make the arithmetic operations in digital system easier. In this article we will discuss about the following topics
1. 9s complement
2. 10s complement
3. 9s complement subtraction
4. 10s complement subtraction
Now first of all let us know what 9's complement is and how it is done. To obtain the 9's complement of any number we have to subtract the number with (10n - 1) where n = number of digits in the number, or in a simpler manner we have to divide each digit of the given decimal number with 9. The table given below will explain the 9's complement more easily.
 Decimal digit 9s complement 0 9 1 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1 9 0

Now coming to 10's complement, it is relatively easy to find out the 10's complement after finding out the 9,s complement of that number. We have to add 1 with the 9,s complement of any number to obtain the desired 10's complement of that number. Or if we want to find out the 10's complement directly, we can do it by following the following formula, (10n - number), where n = number of digits in the number. An example is given below to illustrate the concept of obtaining 10’s complement

Let us take a decimal number 456, 9's complement of this number will be 10's complement of this no 9's complement subtraction We will understand this method of subtraction via an example A = 215 B = 155 We want to find out A-B by 9's complement subtraction method