Tools to code/decode in BCD (binary coded decimal) a numeration system used in electronics and computer systems to code decimal numbers on 4 bits.

Binary Coded Decimal (BCD) - dCode

Tag(s) : Electronics

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Tools to code/decode in BCD (binary coded decimal) a numeration system used in electronics and computer systems to code decimal numbers on 4 bits.

**BCD** (binary coded decimal) encoding replaces directly digits 0, 1, 2, ..., 9 by their binary values (with 4 bits)

0 | 0000 |

1 | 0001 |

2 | 0010 |

3 | 0011 |

4 | 0100 |

5 | 0101 |

6 | 0110 |

7 | 0111 |

8 | 1000 |

9 | 1001 |

__Example:__ To code 123, replace 1 by 0001, 2 by 0010 and 3 by 0011, so 123 is coded 0001,0010,0011 in **BCD**

In computers, storage is done on 8 bits, and to store **BCD** 4 bits on 1 byte (8 bits) is done by filling with 0 or 1 (recommended) at the beginning (storage called extended **BCD**, used in particular by EBCDIC)

__Example:__ The storage of 123 in extended **BCD** is 11110001 11110010 11110011 (completed with 1111 at the start of the byte)

In order not to lose space, there is the **packed BCD** which stores 2 4-bit digits on an 8-bit byte. In addition, the condensed

+ | 1010 | A |

- | 1011 | B |

+ | 1100 | C |

- | 1101 | D |

+ | 1110 | E |

unsigned | 1111 | F |

__Example:__ The storage of 123 in packed **BCD** is 00010010 00111100 (completed with + 1100 at the end if the number of digits is odd)

There are several ways to code + and - because several variants of **BCD** have been proposed by computer manufacturers like IBM or Burroughs.

**BCD** conversion replaces each 4-bit group (packed **BCD**, the most common encoding) by its corresponding digit

__Example:__ 0001 0010 0011 is decoded 1,2,3

If the code is extended **BCD**, the first 4 binary bits of each byte can be ignored.

The message has a length multiple of 4 and non of the 4-bits group can contain 1111.

Some systems uses 1100 for + and 1101 for -

__Example:__ -5 is then written 1101 0101

There are different approaches to writing a non-integer (floating point) number.

The most common method is to use fixed point numbers where the point position is fixed a priori.

__Example:__ It is decided that numbers are stored with 2decimal places (2 digits after the decimal point), then a **BCD** value 123 will then be read 1.23

Another method is used on some systems that use one of the non-digit values (such as 1100, 1101 or 1110) to store the position of the point.

**BCD** is often used in electronics, for storing or displaying numeric values. Conversion is easy, does not need a processor and is similar to peripherals such as 7-segment displays.

Another example is the storing of Dates in a BIOS of a motherboard, still today in **BCD**.

Also the *DECIMAL* format of the fields of certain databases can use this **BCD** coding.

Unused values are 1010, 1011, 1100, 1101, 1110, 1111

The first uses of the **BCD** date from a period between 1950 and 1960

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- BCD Decoder/Converter
- DBC Encoder/Converter
- How to encrypt using BCD coding
- How to decrypt BCD coding
- How to recognize an BCD ciphertext?
- How to write a negative number?
- How to write a non-integer number?
- What is BCD purpose?
- What are BCD values non used in decimal representations?
- When BCD have been invented?

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