Excess-3 Code in Digital Electronics

Excess-3 code is an example of unweighted code. Excess-3 equivalent of a decimal number is obtained by adding 3 and then converting it to a binary format. For instance to find excess-3 representation of decimal number 4, first 3 is added to 4 to get 7 and then binary equivalent of 7 i.e. 0111 forms the excess-3 equivalent.

Below is  table representing excess-3 equivalent of decimal numbers (0-9):

Decimal Number

Excess-3 Equivalent

0

0011

1

0100

2

0101

3

0110

4

0111

5

1000

6

1001

7

1010

8

1011

9

1100

Excess-3 code is also known as self complimenting code or reflective code, as 1′s compliment of any number (0-9) is available within these 10 numbers. For example 1′s complement of 9 (1100) is 0011.

Addition of two numbers in Excess-3 Code

Let’s understand it by taking few examples:

Example 1:

    0101 (2)
  + 1000 (5)
  ---------
    1101 (10)

The result 1101 is in excess-6. To obtain an excess-3 equivalent, binary 3 needs to be subtracted from the result as below:

   1101 (10)
 - 0011 (3)
 --------
   1010 (7)

Example 2:

   1111 1
   0101 1100 (29)
 + 0110 1100 (39)
  --------------
   1100 1000 (95)

Considering that 4 leftmost significant bits form column 1 and 4 rightmost significant bits form column 2. If carry is generated in addition, excess-3 equivalent is obtained by adding binary equivalent of 3 to the column generating carry and subtracting binary equivalent of 3 from the column that doesn’t generate any carry.

In this example, carry is generated by column 1 and no carry is generated by column 2. Thus, excess-3 equivalent is calculated as follows:

    1100    1000 (95)
  - 0011  + 0011
   --------------
    1001    1011 (68)

For excess-3 addition of decimal numbers, first convert the decimal numbers into binary and then perform the addition as explained above.

Hope you find the information presented here useful. Feel free to leave your footprints in the comments section below for any queries or suggestions.

    • Hi Girish,

      Excess-3 code is binary only. Binary means any number can be represented using 0 and 1. As defined by Wiki, Excess-3 binary-coded decimal code is also called as biased representation. It was used on some older computers with a pre-specified number 3 as a biasing value. It is a way to represent values with a balanced number of positive and negative numbers.
      The advantage of excess-3 code over bcd code is that it is easy to find 1′s complement (just by inverting bits) for binary numbers for subtraction.

      Let us know if you have further queries on this. Thank you for stopping by.

  1. Hi,
    Please explain this to me.
    My understanding is that i
    can add a 3 to any number and
    convert to binary. What kind of
    Numbers am I allowed to add a 3
    To?

    • Hi Mots,

      Your understanding is correct. Just to be precise, you can add 3 to any “decimal” number and convert it to binary. So in your words, you are allowed to add a 3 to decimal number to get it’s excess-3 equivalent.

      Hope that helps. Let us know.

  2. Hi Rishwa,

    For an Excess-N number, N is the excess amount and N is added to the decimal number. Similarly, for an Excess-3 number, 3 is the excess amount and hence 3 is added to the decimal number to get an excess-3 equivalent.

    Hope the answer clarifies your doubt.

    Regards

  3. Its simple…!! thanks for that……!

    But why to add 3 to the column generating carry and subtract 3 to the column with no carry generated ????
    help me please..!!!

  4. it is difficult to write 45326 equivalent binary number
    so we use BCD(binary coded decimal number)
    decimial (0-9) will represent in binary
    so 4 5 3 2 6
    0100 0101 0011 0010 0110
    if we know 0t0 9 equivalent binary number we can represent any number

  5. Hi Lavaynya,

    We have provided only a snapshot of excess-3 codes here. You surely can write excess-3 codes for numbers greater than 9.

    Let us know for any further queries.

  6. Hi Amit,

    We have explained above to Rishwa:

    For an Excess-N number, N is the excess amount and N is added to the decimal number. Similarly, for an Excess-3 number, 3 is the excess amount and hence 3 is added to the decimal number to get an excess-3 equivalent.

    Hope the answer clarifies your doubt.

    Regards

  7. Whats the main use of excess 3 code in digital elecronics? Is there a similarity between excess 3 code and parity bits?

  8. Hi Rohit,

    We have explained in the post above. Please let us know of any specific queries you have.

    Regards

  9. if we try to find excess 3 code of 108 by adding 333 to it we get answer 010001000001 but on the another way if i firrt convert 108 into excess 3 nd them add binary equivalent of 3 into it then answer will be 010000111011 then my question is that why such diff. is come ie one method is wrong then plz tell me which method is write

  10. Hi Rajni,

    You should first find excess-3 equivalent of 108 and 333. Now add excess-3 equivalents of 108 and 333 and adjust the sum as shown in example 1 and 2 above.

    Regards

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