Self Complementing Codes in Digital Logic Design | Explained with Examples

Self-complementing codes are a special type of weighted binary codes in which the 9’s complement (or 1’s complement in binary) of a decimal digit can be obtained just by inverting (complementing) each bit of its code word.

👉 In other words:
If a code is self-complementing, then the code for digit 𝑑 and the code for digit 9−𝑑 are bitwise complements of each other.

Key Properties

The sum of the weights of the code = 9 (this ensures the complement property works correctly).
Very useful in decimal arithmetic (e.g., subtraction using 9’s complement).
Used in digital systems for error detection and simplification of operations.
Examples of Self-Complementing Codes

✅ Excess-3 (XS-3) Code

A non-weighted code but self-complementing.

Each decimal digit = its 8421 BCD + 3.

Example:

Decimal 2 → 0101 (Excess-3)

Decimal 7 → 1010 (Excess-3)

Notice: 2 and 7 are complements (2 + 7 = 9), and their codes are bitwise complements.

✅ 2421 Code

Weighted code with weights (2, 4, 2, 1).

Example:

Decimal 3 → 0011 (2421)

Decimal 6 → 1100 (2421)

Codes are complements.
✅ 84-2-1 Code

Weighted code with weights (8, 4, –2, –1).

Also self-complementing.
Learn about self-complementing codes in digital electronics with clear examples.
Understand why Excess-3 code, 2421 code, and 84-2-1 code are called self-complementing codes, and how they are different from BCD (8421 code). Perfect for students of Digital Logic Design (DLD), Computer Organization, and Electronics Engineering.

self complementing codes

self complementing codes in digital logic design

excess-3 code explained

2421 code in digital electronics

84-2-1 code

examples of self complementing codes

weighted and non-weighted codes

difference between BCD and excess-3 code

digital codes tutorial

DLD important questions