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Hex to Quaternary converter

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How to convert Hex to Quaternary

Hexadecimal is a positional system that represents numbers using a base of 16. Unlike the common way of representing numbers with ten symbols, it uses sixteen distinct symbols, most often the symbols "0"-"9" to represent values zero to nine, and "A"-"F" to represent values ten to fifteen. Hexadecimal numerals are widely used by computer system designers and programmers, as they provide a human-friendly representation of binary-coded values.

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 hexadecimal number into quaternary form:

The simplest way is to convert the hexadecimal number into decimal, then the decimal into quaternary form.
  1. Write the powers of 16 (1, 16, 256, 4096, 65536, and so on) beside the hex digits from bottom to top.
  2. Convert any letters (A to F) to their corresponding numerical form.
  3. Multiply each digit by it's power.
  4. Add up the answers. This is the decimal solution.
  5. Divide the decimal number by 4.
  6. 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).
  7. Keep a note of the remainder, it should be between 0 and 3.
  8. Repeat the steps from step 5. until the quotient is equal to 0.
  9. Write out all the remainders, from bottom to top. This is the quaternary solution.
For example if the given hexadecimal number is 29C:
C (12)112
Then the decimal solution (512 + 144 + 12) is: 668
668 / 41670
167 / 4413
41 / 4101
10 / 422
2 / 402
Finally the quaternary solution is: 22130
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