Tool for decoding/encoding numbers via the Stibitz code also called Excess-3, a binary digital system similar to the BCD code, used by old processors coding each digit on 4 bits.
Excess-3 Code (Stibitz) - dCode
Tag(s) : Character Encoding
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Excess-3 Code (Stibitz)
Excess-3 Decoder/Converter
Excess-3 Encoder/Converter
Answers to Questions (FAQ)
What is Excess3 code? (Definition)
The code Excess-3 (also called Stibitz code and sometimes shortcut XS3 or XS-3) is a 4-bit binary decimal code (like the BCD) created to optimize some calculations in base 10 on older processors.
How to encrypt using Excess3 code?
The representation of a number in Excess-3 code is said to be biased because it has an offset of 3 (hence the 3 of XS-3) with the expected values and used by the conventional BCD code.
Example: 0 is coded 0011 in XS-3 whereas 0011 is 3 in BCD code.
The use of this offset allows a quick calculation trick for the complement to 9 (decimal) by inverting the bits, which is a big time saver for the calculation of subtractions by the processors.
Example: The digit 0 is coded 0011 in XS3 and its binary complement (inverting the 1's and 0's) is 1100 which corresponds to 9 in XS3.
The Decimal to Excess-3 conversion table/equivalence:
| Digit | Code XS-3 |
|---|---|
| 0 | 0011 |
| 1 | 0100 |
| 2 | 0101 |
| 3 | 0110 |
| 4 | 0111 |
| 5 | 1000 |
| 6 | 1001 |
| 7 | 1010 |
| 8 | 1011 |
| 9 | 1100 |
Example: 123 is coded 0100,0101,0110
The codes 0000 or 1111 are not used to represent numbers, which can be interesting in the sending of communication (the sequences of 0 and 1 are often representative of reading errors)
How to convert a number coded in Excess3?
Split the binary number into groups of 4 bits and replace each group with the corresponding number in the conversion table (above).
Example: 11001011 is split 1100,1011 and corresponds respectively to the numbers 9,8, so the conversion into decimal is 98
How to recognize an Excess3 coded number?
The code has a binary representation, it is not really distinguishable from another binary code (BCD, Gray, etc.) apart from its particularity to avoid sequences of more than 7 0000000 or 1111111.
Any reference to the old processors, calculators or electronic cash machines of the 70s is a clue.
When was Excess-3 invented?
George Stibitz created a calculating machine based on this principle in 1937.
Source code
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Excess-3 Code (Stibitz) on dCode.fr [online website], retrieved on 2024-12-19,
