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Quaternary to Hex converter

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How to convert Quaternary to Hex

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.

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.


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

The simplest way is to convert the quaternary number into decimal, then the decimal into hexadecimal form.
  1. Write the powers of 4 (1, 4, 16, 64, 256, and so on) beside the quaternary 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 16.
  5. Get the integer quotient for the next iteration (if the number will not divide equally by 16, then round down the result to the nearest whole number).
  6. Keep a note of the remainder, it should be between 0 and 15.
  7. Repeat the steps from ftep 4. until the quotient is equal to 0.
  8. Write out all the remainders, from bottom to top.
  9. Convert any remainders bigger than 9 into hex letters. This is the hex solution.
For example if the given quaternary number is 3021:
Then the decimal solution (192 + 8 + 1) is: 201
201 / 16129
12 / 16012 (C)
Finally the hexadecimal solution is: C9
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