Decimal Number | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

Octal Number | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 20 | 21 | 22 | 23 | 24 |

The octal system is radix-8, this system uses the numerals 0-7. This system is a great thing to know. When you're using the octal system, you can at a glance, know what number you are looking at in binary. Every three binary columns are an octal number. Let's look at a table:

Binary Number | Decimal Equivalent | Octal Equivalent |

101101 | 32 + 8 + 4 + 1 = 45_{10} |
55_{8} = 5 * 8_{10} + 5 = 45_{10} |

111100 | 32 + 16 + 8 + 4 = 60_{10} |
74_{8} = 7 * 8_{10} + 4 = 45_{10} |

Every three binary columns can go from 0 - 7 in magnitude. This means you are either staring at a 1's column, a 2's column, or a 4's column. Every set of three
to the left over you go, you add a * 8. (*C*^{n}).

Where: c= columns to shift over, and n = power of set, with the exception of the first set where n = 0 (the 1's set)

/ ∞ \

| ∑ (c + 3) | ÷ 3 = n

\ c = 3 /

So let's break it down in another table:

Binary Number | Octal Sets | Conversion Equivalent |

10110101 | 10 110 101 | 2 * 8^{2}_{10} + 6 * 8^{1}_{10} + 5 * 8^{0}_{10} = 181_{10} |

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