## How to convert Quaternary to Quinary

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.Quinary is a numeral system with five as the base. A possible origination of a quinary system is that there are five fingers on either hand. In the quinary place system, five numerals, from 0 to 4, are used to represent any real number. According to this method, five is written as 10, twenty-five is written as 100 and sixty is written as 220.

**Formula**

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

The simplest way is to convert the quaternary number into decimal, then the decimal into quinary 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 5.
- Get the integer quotient for the next iteration (if the number will not divide equally by 5, then round down the result to the nearest whole number).
- Keep a note of the remainder, it should be between 0 and 4.
- 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 quinary solution.

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

2 | 64 | 128 |

0 | 16 | 0 |

3 | 4 | 12 |

3 | 1 | 3 |

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

143 / 5 | 28 | 3 |

28 / 5 | 5 | 3 |

5 / 5 | 1 | 0 |

1 / 5 | 0 | 1 |