How to convert Hex to Octal
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.The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal is sometimes used in computing instead of hexadecimal, perhaps most often in modern times in conjunction with file permissions under Unix systems. It has the advantage of not requiring any extra symbols as digits. It is also used for digital displays.
Formula
Follow these steps to convert a hexadecimal number into octal form:
The simplest way is to convert the hexadecimal number into decimal, then the decimal into octal 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 8.
- Get the integer quotient for the next iteration (if the number will not divide equally by 8, then round down the result to the nearest whole number).
- Keep a note of the remainder, it should be between 0 and 7.
- 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 octal solution.
| Digit | Power | Multiplication |
|---|---|---|
| B (11) | 256 | 2816 |
| 8 | 16 | 128 |
| A (10) | 1 | 10 |
| Division | Quotient | Remainder |
|---|---|---|
| 2954 / 8 | 369 | 2 |
| 369 / 8 | 46 | 1 |
| 46 / 8 | 5 | 6 |
| 5 / 8 | 0 | 5 |