Binary to Excess-3 Converter
Convert binary numbers into Excess-3 (XS-3 / Stibitz) self-complementing code. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.
Enter binary sequence (e.g. 1001 for 9).
Calculated Output
Step-by-Step Mathematical Proof
Active DerivationWhat Is Binary to Excess-3 Converter?
Excess-3 code (XS-3 or Stibitz code) is an unweighted, self-complementing digital encoding formed by adding 3 (binary 0011) to each digit of an 8421 BCD number.
How Does It Work?
Convert the binary number to its decimal digits. Add 3 to each decimal digit (d + 3), then convert each resulting sum into a 4-bit binary nibble.
Mathematical Algorithm
Step-by-Step Example
Important Rules & Edge Cases
- Every decimal digit maps to a 4-bit nibble from 0011 (0+3) to 1100 (9+3).
- It is self-complementing: bitwise inverting an XS-3 code produces the 9’s complement of the decimal digit.
Practical Applications in Engineering
- Arithmetic simplification in early electromechanical and decimal computers.
- Fast decimal 9’s complement generation without borrow circuitry.
- Educational instruction in digital logic coding.
Common Mistakes to Avoid
- Caution: Adding 3 to the total binary number instead of adding 3 to each individual decimal digit.
- Caution: Allowing nibble sums greater than 1100 (12).
Frequently Asked Questions
Why is Excess-3 called a self-complementing code?
Because taking the 1’s complement (inverting all bits) of an Excess-3 nibble automatically yields the Excess-3 code of that digit’s 9’s complement (e.g. inverting 0 gives 9).
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