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Decimal to Quaternary converter

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How to convert Decimal to Quaternary

The decimal numeral system is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu-Arabic numeral system. For writing numbers, the decimal system uses ten decimal digits, a decimal mark, and, for negative numbers, a minus sign "-". The decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; the decimal separator is the dot "." in many countries.

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 decimal number into quaternary form:
  1. Divide the decimal number by 4.
  2. 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).
  3. Keep a note of the remainder, it should be between 0 and 3.
  4. Repeat the steps until the quotient is equal to 0.
  5. Write out all the remainders, from bottom to top. This is the solution.
For example if the given decimal number is 395:
DivisionQuotientRemainder
395 / 4983
98 / 4242
24 / 460
6 / 412
1 / 401
Then the quaternary solution is: 12023
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