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.
Formula
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.
- Write the powers of 16 (1, 16, 256, 4096, 65536, and so on) beside the hex digits from bottom to top.
- Convert any letters (A to F) to their corresponding numerical form.
- 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 5. until the quotient is equal to 0.
- Write out all the remainders, from bottom to top. This is the quaternary solution.
| Digit | Power | Multiplication |
|---|---|---|
| 2 | 256 | 512 |
| 9 | 16 | 144 |
| C (12) | 1 | 12 |
| Division | Quotient | Remainder |
|---|---|---|
| 668 / 4 | 167 | 0 |
| 167 / 4 | 41 | 3 |
| 41 / 4 | 10 | 1 |
| 10 / 4 | 2 | 2 |
| 2 / 4 | 0 | 2 |