A self-complementing code is one in which the 9's complement is formed by taking the 1's complement. For instance, the 9's complement of 6 is 3 and the 9's complement of 1 is 8.
If we consider Excess 3:
0 0011
1 0100
2 0101
3 0110
4 0111
5 1000
6 1001
7 1010
8 1011
9 1100
If we consider Excess 3:
0 0011
1 0100
2 0101
3 0110
4 0111
5 1000
6 1001
7 1010
8 1011
9 1100
Then thinking about 6 and 3 we see the XS3 codes are: 1001 and 0110 which are the 1's complement of each other. Considering 1 and 8, the XS3 codes are 0100 and 1011 - again 1's complements. There are several self-complementing codes. There is one where instead of the usual binary weights of 8, 4, 2 and 1 you can use 2, 4, 2, and 1.
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