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Quinary to Quaternary converter

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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.


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.
  1. Write the powers of 5 (1, 5, 25, 125, 625, and so on) beside the quinary digits from bottom to top.
  2. Multiply each digit by it's power.
  3. Add up the answers. This is the decimal solution.
  4. Divide the decimal number by 4.
  5. 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).
  6. Keep a note of the remainder, it should be between 0 and 3.
  7. Repeat the steps from step 4. until the quotient is equal to 0.
  8. Write out all the remainders, from bottom to top. This is the quaternary solution.
For example if the given quinary number is 1322:
Then the decimal solution (125 + 75 + 10 + 2) is: 212
212 / 4530
53 / 4131
13 / 431
3 / 403
Finally the quaternary solution is: 3110
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