## How to convert Quinary to Quaternary

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.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.

**Formula**

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

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

- Write the powers of 5 (1, 5, 25, 125, 625, and so on) beside the quinary 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 4.
- Get the integer quotient for the next iteration (if the number will not divide equally by 4, then round down the result to the nearest whole number).
- Keep a note of the remainder, it should be between 0 and 3.
- 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 quaternary solution.

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

1 | 125 | 125 |

3 | 25 | 75 |

2 | 5 | 10 |

2 | 1 | 2 |

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

212 / 4 | 53 | 0 |

53 / 4 | 13 | 1 |

13 / 4 | 3 | 1 |

3 / 4 | 0 | 3 |