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):

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.