The binary number system is base 2. The only numbers in the system are 0 and 1.

In binary, numbering follows powers of 2 instead of powers of 10 like in decimal.

Decimal: 1^{1000}2^{100}3^{10}4^{1} = 1234

Binary: 1^{8}1^{4}1^{2}1^{1} = 15

Binary: 1

If a 0 is present, the value is not counted since 0 to any power is still 0.

Decimal |
Binary |

0 | 0000 |

1 | 0001 |

2 | 0010 |

3 | 0011 |

4 | 0100 |

5 | 0101 |

6 | 0110 |

7 | 0111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

11 | 1011 |

12 | 1100 |

13 | 1101 |

14 | 1110 |

15 | 1111 |

For purposes of understanding IPv6 addressing, it is not necessary to be familiar with anything higher than the table above.

Hexadecimal:

Unlike base 10 which most people are used to, hexadecimal is base 16. So instead of carrying a 1 after counting to 9 like in decimal, you will instead place an A and go through F.

Decimal | Hexadecimal |

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 |

F is the final letter used in hexadecimal notation. After F, hexadecimal operates like base 10 in that you carry a 1. Ex: C D E F 10 11 12 … 1F 20 21 22, etc

A bit is defined as a binary digit. This means a bit can either be 0 or 1.

A nibble is comprised of 4 bits. Ex: 0011, 0101, etc.

Bits and nibbles are important in understanding how hexadecimal notation works. Each hexadecimal digit is one nibble. So in the previous table 3 = 0011, 7 = 0111, B = 1011, etc.

To convert from a string of bits to hexadecimal, first group the bits into nibbles:

A nibble is comprised of 4 bits. Ex: 0011, 0101, etc.

Bits and nibbles are important in understanding how hexadecimal notation works. Each hexadecimal digit is one nibble. So in the previous table 3 = 0011, 7 = 0111, B = 1011, etc.

To convert from a string of bits to hexadecimal, first group the bits into nibbles:

Initial string: 0011110110000000

Separated into nibbles: 0011 1101 1000 0000

Separated into nibbles: 0011 1101 1000 0000

Finally convert each nibble into its hexadecimal equivalent:

Hexadecimal string: 3 D 8 0

Referenced from: IPv6

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