*radix complement system*also known as

*r’s complement system*.

r stands for radix which is a base for a number in a particular number system.

Examples of number system are *decimal, binary, octal, hexadecimal.*

For example,

If you talk about binary system, the base is 2, then we have two types of *r’s* complement.

- r’s complement
- (r-1)’s complement

For decimal number the* r’s* complement is *10’s* complement and *(r-1)’s* complement is *9’s *complement because base is 10.

To subtract using *10’s* complement . Check this example .

**Q1. Subtract using 10’s complement 52 – 12 .**

We know that *52 – 12 = 40*

Let *m = 52* and * n = 12*

Take *10’s* complement of *12*

* 99** – 12**______** 87 **______*

Now, *87* is *9’s *complement because we subtracted it with *99*. To make it *10’s *complement add 1 to *87*. The *10’s *complement of *12* is *88.*

Add the* 88* to *m** 52**+88**______*~~1~~ 40*______ *

Answer : *40*

**Check the second example , **

** Q2: Subtract using 10’s complement 12 – 52**

**We know that 12 < 52 , so answer is -40**

Let *m = 12* and *n = 52*

*10’s* complement of *52*

* 99**-52**______** 47**______*

The* 9’s *complement of* 52* is *47. *To make it *10’s* complement add *1 *to *47.*

Add *48* to *m*

* 12**+48**_____ ** 60**_____*

This is not the answer , wait

Take one more *10’s* complement of the result.* 99**-60**____ ** 39*

____

The *9’s* complement of *60* is *39*. Add *1* to *39* and make is *10’s *complement.

Add negative to the result because *m > n.*

**Answer: -40**

**Summary**

How do I take *10’s* complement ?

Suppose *n = 123* then

There are 3 digits in *123*.The* 10’s *complement would be *9’s* compliment* + 1.*

*999 – 123 = 876 **876 + 1 = 877*

Therefore, the 10’s complement of *123* is *877.*