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) : Informatics

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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.

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.

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:

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)

Splut 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 in decimal is 98

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 machine of the 70s is a clue.

George **Stibitz** created a calculating machine based on this principle in 1937.

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