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What is Excess 3 codes? Why it is called as self complementary code.

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What is Excess 3 codes? Why it is called as self complementary code.

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written 5.6 years ago by | • modified 5.6 years ago |

Excess 3 codes are also called as **XS-3** code.

- Excess 3 codewords are derived from the
**8421 BCD**code words by adding $(0011)_{2}$ or $(3)_{10}$ to each codeword in**8421**. The Excess-3 code is obtained as follows

Decimal Number $\rightarrow$ 8421 BCD $\frac{Add}{0111}$ Excess-3 code

** Note:-** Excess-3 is a sequential code because each succeeding code is one binary number greater than its preceding code.

Decimal | BCD 8421 | Excess-3 BCD+8421(0110) |
---|---|---|

0 | 0000 | 0011 |

1 | 0001 | 0100 |

2 | 0010 | 0101 |

3 | 0011 | 0110 |

4 | 0100 | 0111 |

5 | 0101 | 1000 |

6 | 0110 | 1001 |

7 | 0111 | 1010 |

8 | 1000 | 1011 |

9 | 1001 | 1100 |

Excess-3 is a sequential code because we get any codeword by adding binary '1' to its previous codewords

Excess-3 is a self-complementing code. This is because in Excess-3 code we get the 9's complement of a number by just complementing each bit that means by replacing a '0' by '1' and '1' by '0'

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