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BCD Addition:

 

In BCD, maximum number that can be represented is 9 i.e. 1001. [1010, 1011, 1100, 1101, 1110, 1111 are invalid in BCD representation].

For addition of BCD number, it may cause some problem when output is out of range.

 

Example:

 

 

Let take another example:

 

 

It is invalid in BCD because 1010 is 10

 

Whenever we get any invalid pattern, we add 6 i.e. (0110) to correct it.

 

 

Note: If we get carry after adding 6 then take it as a number separately.

 

 

Whenever we are adding any BCD digits, 3 possible cases can appear:

 

Now the question is why we add 6 when an error occurred as an invalid number:

As we know only 0 to 9 is valid at BCD so, when we get an invalid range we add 6 to get a valid range again. 

 

 

Example:

 

 

If we see the answer 0010 that is 2 which is valid in BCD, but it has a carry 1. It has an error.

[As we know if the addition of BCD is valid, but there is carry at the output, then still we add 6 to make the exact valid number.]

 

To correct it we have to add 6 i.e. (0110) to correct it.

 

Note: Again we got a carry but as we discussed earlier if we get carry after the addition of 6 it is not an error, take it as a separate number. 

So,

 

 

We take another big example

So, we add 6 (i.e. 0110) in invalid answers.