The Excess-3 decimal code is a self-complementing code because
Complement can be generated by inverting each bit pattern.
A decimal code is self-complementing when the code word of the 9’s complement of a digit (that is, of \(9 - d\)) is obtained simply by inverting every bit of the code word of d.
In Excess-3, each digit d is coded as the 4-bit binary of \(d + 3\). For example, 2 is 0101 and its 9’s complement 7 is 1010, which is exactly 0101 with every bit inverted; similarly 0 is 0011 and 9 is 1100.
This works because \((d + 3) + (9 - d + 3) = 15 = 1111_2\), so the two code words always add to 1111 and are bitwise complements of each other.
The binary sum of a code word and that of its 9’s complement is 1111 (15), not 9, and nothing relates the 10’s complement in this way. Excess-3 is also not a weighted code, since no fixed position weights produce it.
Hence, the answer is Complement can be generated by inverting each bit pattern..
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