# Hexadecimal

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### Why Hexadecimal?

The link between binary and hexadecimal is intimate. Here's the list of binary numbers for the 16 unique hexadecimal (or "hex" for short) symbols and their base 10 equivalents:

Binary |
Hexadecimal |
Base 10 |

0000 |
0 |
0 |

0001 |
1 |
1 |

0010 |
2 |
2 |

0011 |
3 |
3 |

0100 |
4 |
4 |

0101 |
5 |
5 |

0110 |
6 |
6 |

0111 |
7 |
7 |

1000 |
8 |
8 |

1001 |
9 |
9 |

1010 |
A |
10 |

1011 |
B |
11 |

1100 |
C |
12 |

1101 |
D |
13 |

1110 |
E |
14 |

1111 |
F |
15 |

Notice how 4 bits can be summarized with a single Hex character. For just 4 bits, this looks like more work than it's worth. However, when we start looking at long strings of numbers, the compactness of Hexadecimal, it's aligned correspondence of 4 bits to 1 symbol, and the related freedom from having to do multiplication and addition to convert back and forth between bases (compare converting from binary to decimal and back) Hex is the most convenient number system with which to work. As we will see, typical conversions between digital and analog representations of quantities use between 8 and 24 bits. At 8 bits, maybe just writing down the bits is adequate. However, 24 bits is a difficult for people to deal with. 24 bits can be expressed as 24/4 = 6 Hex characters. That's much more reasonable.