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.
Formula
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.
- Write the powers of 4 (1, 4, 16, 64, 256, and so on) beside the quaternary digits from bottom to top.
- Multiply each digit by it's power.
- Add up the answers. This is the decimal solution.
- Divide the decimal number by 16.
- 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).
- Keep a note of the remainder, it should be between 0 and 15.
- Repeat the steps from ftep 4. until the quotient is equal to 0.
- Write out all the remainders, from bottom to top.
- Convert any remainders bigger than 9 into hex letters. This is the hex solution.
| Digit | Power | Multiplication |
|---|---|---|
| 3 | 64 | 192 |
| 0 | 16 | 0 |
| 2 | 4 | 8 |
| 1 | 1 | 1 |
| Division | Quotient | Remainder |
|---|---|---|
| 201 / 16 | 12 | 9 |
| 12 / 16 | 0 | 12 (C) |