Decode/Encode Decimal to BCD - Binary Coded Decimal

VIDEO guide BCD to decimal at the end

BCD to DEC

To use this online BCD to DEC converter tool, type a BCD value like 1E into the left field below, and then hit the Convert button.

You can convert up to 16 BCD
characters (max. value of 7fffffffffffffff) to decimal.

BCD (binary Coded Decimal) number:

DEC to BCD

To use this online BCD to decimal converter tool, type a decimal value like 999 into the field below, and then hit the Convert button. You can convert up to 10 decimal characters (max. value of 9999999999999999) to BCD.)

DEC (decimal) number:

A regular decimal number is the sum of the digits multiplied with power of 10.

137 in base 10 is equal to each digit multiplied with its corresponding power of 10:

137_{10} = 1×10^{2}+3×10^{1}+7×10^{0} = 100+30+7

BCD numbers are read the same way, but each digit counts power of 16 instead of power of 10.

For BCD number with n digits:

*d _{n-1} ... d_{3} d_{2} d_{1} d_{0}*

Multiply each digit of the BCD number with its corresponding power of 16 and sum:

decimal = *d _{n-1}×16^{n-1}+...+d_{3}×16^{3}+d_{2}×16^{2}+d_{1}×16^{1}+d_{0}×16^{0}*

3B in base 16 is equal to each digit multiplied with its corresponding 16^{n}:

3B_{16} = 3×16^{1}+11×16^{0} = 48+11 = 59_{10}

E7A9 in base 16 is equal to each digit multiplied with its corresponding 16^{n}:

E7A9_{16} = 14×16^{3}+7×16^{2}+10×16^{1}+9×16^{0} =
57344+1792+160+9 = 59305_{10}

0.8 in base 16:

0.8_{16} = 0×16^{0}+8×16^{-1} = 0+0.5 = 0.5_{10}

Decimal | BCD |
---|---|

0 | 0 |

1 | 1 |

2 | 2 |

3 | 3 |

4 | 4 |

5 | 5 |

6 | 6 |

7 | 7 |

8 | 8 |

9 | 9 |

10 | A |

11 | B |

12 | C |

13 | D |

14 | E |

15 | F |

**Decimal** number system is the most commonly used and the most familiar one to the general public. It is also known as *Base 10 numbering* system
since it is based on 10 following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. In decimal system, every digit has its own position as well as the decimal point. I.e. the
number 356.74 has 4 in the Hundredths position, 7 in the Tenths position, 6 in the Units position, 5 in the Tens position, and 3 in the Hundreds position. *Decimal
number system* is also one of the oldest known numeral system, which is historically related to Hindu-Arabic numeral system.

**Hex**, or *hexadecimal*, is a number system of base 16. This number system is especially interesting because in our casually used decimal system
we have only 10 digits to represent numbers. As hex system has 16 digits, the extra needed 6 digits are represented by the first 6 letters of English alphabet. Hence, **hex**
digits are 0,1,2,3,4,5,6,7,8 and 9 A, B, C, D, E, F. This number system is the most commonly used in mathematics and information technologies. I.e. in html programming
colors can be represented by a 6-digit *hexadecimal number*: FFFFFF represents white, 000000 represents black, and so on.

- (79)
_{10}= (4F)_{16} - (120)
_{10}= (78)_{16} - (1728)
_{10}= (6C0)_{16}