The Excess-3 decimal code is a self-complementing code because
2014
The Excess-3 decimal code is a self-complementing code because
- A.
The binary sum of a code and its 9’s complement is equal to 9.
- B.
It is a weighted code.
- C.
Complement can be generated by inverting each bit pattern.
- D.
The binary sum of a code and its 10’s complement is equal to 9.
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Correct answer: C
Key idea: In Excess-3 each decimal digit d is encoded as the 4-bit binary representation of (d + 3).
Let code(d) = binary(d + 3) using 4 bits.
Invert all bits (bitwise complement): this yields value 15 − (d + 3) = 12 − d.
Observe that 12 − d = (9 − d) + 3, so the inverted pattern equals code(9 − d).
Therefore, inverting each bit of an Excess-3 code gives the Excess-3 code of the 9's complement digit; this is why Excess-3 is self-complementing.
Example: digit 2 → code = binary(2 + 3) = binary(5) = 0101. Invert bits → 1010, which is binary(10) = code(7) since 7 = 9 − 2.
Conclusion: Bitwise inversion maps each digit's code to the code of its 9's complement, so Excess-3 is self-complementing.