Number Converting:

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Converting from octal to binary is as easy as converting from binary to octal. Simply look up each octal digit to obtain the equivalent group of three binary digits.

Octal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

Binary: | 000 | 001 | 010 | 011 | 100 | 101 | 110 | 111 |

Octal = | 3 | 4 | 5 | |

Binary = | 011 | 100 | 101 | = 011100101 binary |

When converting from octal to hexadecimal, it is often easier to first convert the octal number into binary and then from binary into hexadecimal. For example, to convert 345 octal into hex:

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Octal = | 3 | 4 | 5 | |

Binary = | 011 | 100 | 101 | = 011100101 binary |

Drop any leading zeros or pad with leading zeros to get groups of four binary digits (bits):

Binary 011100101 = 1110 0101

Then, look up the groups in a table to convert to hexadecimal digits.

Binary: | 0000 | 0001 | 0010 | 0011 | 0100 | 0101 | 0110 | 0111 |

Hexadecimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

Binary: | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 |

Hexadecimal: | 8 | 9 | A | B | C | D | E | F |

Binary = | 1110 | 0101 | |

Hexadecimal = | E | 5 | = E5 hex |

Therefore, through a two-step conversion process, octal 345 equals binary 011100101 equals hexadecimal E5.

Converting octal to decimal can be done with repeated division.

- Start the decimal result at 0.
- Remove the most significant octal digit (leftmost) and add it to the result.
- If all octal digits have been removed, you’re done. Stop.
- Otherwise, multiply the result by 8.
- Go to step 2.

Octal Digits | Operation | Decimal Result | Operation | Decimal Result |

345 | +3 | 3 | × 8 | 24 |

45 | +4 | 28 | × 8 | 224 |

5 | +5 | 229 | done. |

The conversion can also be performed in the conventional mathematical way, by showing each digit place as an increasing power of 8.

345 octal = (3 * 8^{2}) + (4 * 8^{1}) + (5 * 8^{0}) = (3 * 64) + (4 * 8) + (5 * 1) = 229 decimal

Converting from hexadecimal is next...