# How are hex codes calculated

## Hexadecimal number system (hex code)

Large binary numbers have the disadvantage that they are very confusing.

To remedy this, the hexadecimal system was introduced.

4 bits of a binary number are replaced by a hexadecimal character.

Since a 4-bit binary number can have 16 states, but we only know 10 decimal numbers, 6 letters have been added to the hexadecimal number system.

**Nominal values:** 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F**Base:** 16**Largest face value:** F.**Significance:** 16^{0} = 1, 16^{1} = 16, 16^{2} = 256, etc.

This table is used for a better understanding of the counting method in the hexadecimal number system. Each 4 binary digits form a hexadecimal digit.

Decimal | Binary / dual | Hexadecimal | |||
---|---|---|---|---|---|

0 | 0 | 0 | 0 | 0 | 0 |

1 | 0 | 0 | 0 | 1 | 1 |

2 | 0 | 0 | 1 | 0 | 2 |

3 | 0 | 0 | 1 | 1 | 3 |

4 | 0 | 1 | 0 | 0 | 4 |

5 | 0 | 1 | 0 | 1 | 5 |

6 | 0 | 1 | 1 | 0 | 6 |

7 | 0 | 1 | 1 | 1 | 7 |

8 | 1 | 0 | 0 | 0 | 8 |

9 | 1 | 0 | 0 | 1 | 9 |

10 | 1 | 0 | 1 | 0 | A. |

11 | 1 | 0 | 1 | 1 | B. |

12 | 1 | 1 | 0 | 0 | C. |

13 | 1 | 1 | 0 | 1 | D. |

14 | 1 | 1 | 1 | 0 | E. |

15 | 1 | 1 | 1 | 1 | F. |

### Hexadecimal numbers in computer engineering

In computer technology, the dual number system is decisive. Sometimes the hexadecimal system is also used. Usually for a clearer representation of large dual numbers. Long bit sequences of 4 bits each are grouped and converted into a hexadecimal number. In this way, a long sequence of 1 and 0 results in a shorter hexadecimal number. For easier readability, hexadecimal numbers are then grouped again in groups of 2 or 4.

Hexadecimal numbers or the hexadecimal representation is another form of representation of bit sequences.

010100001010110000111111 | Bit sequence | |||||
---|---|---|---|---|---|---|

0101 | 0000 | 1010 | 1100 | 0011 | 1111 | grouped bit sequence |

5 | 0 | A. | C. | 3 | F. | Conversion to hex numbers |

50 | AC | 3F | grouped hex numbers |

The hexadecimal system or the sixteen system is used for a clearer and more compact representation of long bit sequences. It is also used in assembler programming for addressing I / O and memory modules.

### Spelling of the hexadecimal numbers

Hexadecimal numbers are marked with a "16" as an index or a preceding dollar sign ($). Other spellings with "h" or "H" are inconsistent and therefore not correct and are only acceptable in exceptional cases.

- 100
_{16}(correct spelling) - $ 100 (correct spelling)
- 0x100 (correct spelling)
- 100h (wrong spelling)
- 100H (incorrect spelling)

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