## How to convert Quaternary to Octal

Quaternary is the base-4 numeral system. It uses the digits 0, 1, 2 and 3 to represent any real number. Four is the largest number within the subitizing range and one of two numbers that is both a square and a highly composite number, making quaternary a convenient choice for a base at this scale. Despite being twice as large, its radix economy is equal to that of binary.The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal is sometimes used in computing instead of hexadecimal, perhaps most often in modern times in conjunction with file permissions under Unix systems. It has the advantage of not requiring any extra symbols as digits. It is also used for digital displays.

**Formula**

Follow these steps to convert a quaternary number into octal form:

The simplest way is to convert the quaternary number into decimal, then the decimal into octal form.

- Write the powers of 4 (1, 4, 16, 64, 256, and so on) beside the quaternary digits from bottom to top.
- Multiply each digit by it's power.
- Add up the answers. This is the decimal solution.
- Divide the decimal number by 8.
- Get the integer quotient for the next iteration (if the number will not divide equally by 8, then round down the result to the nearest whole number).
- Keep a note of the remainder, it should be between 0 and 7.
- Repeat the steps from step 4. until the quotient is equal to 0.
- Write out all the remainders, from bottom to top. This is the octal solution.

Digit | Power | Multiplication |
---|---|---|

1 | 256 | 256 |

3 | 64 | 192 |

0 | 16 | 0 |

2 | 4 | 8 |

3 | 1 | 3 |

Division | Quotient | Remainder |
---|---|---|

459 / 8 | 57 | 3 |

57 / 8 | 7 | 1 |

7 / 8 | 0 | 7 |