Hex to Octal Converter — How to Convert Hexadecimal to Octal
Understand how to perform base-16 to base-8 conversions using the binary grouping method, complete with examples and an interactive calculator.
Try it: Hex to Octal mini-calculator
Why convert via binary?
Direct conversion between hexadecimal (base-16) and octal (base-8) can be difficult to calculate mentally since 16 is not an integer power of 8. The standard and most reliable shortcut is to use binary (base-2) as an intermediate step.
Because 2⁴ = 16 and 2³ = 8, we can easily map hex characters to 4-bit binary chunks, and then regroup those bits into 3-bit chunks to find the corresponding octal values.
The conversion steps.
- Convert each hexadecimal digit to its equivalent 4-bit binary group (see mapping chart).
- Combine all the 4-bit groups into a single binary string.
- Group the binary bits into sets of three starting from the right (least significant digit). Add leading zeros to the leftmost group if necessary.
- Convert each 3-bit binary group to its corresponding octal digit (0-7).
Step-by-step examples.
Example 1: Convert Hex 7C to Octal
- Convert hex digits to 4-bit binary groups:
7 ➔ 0111,C ➔ 1100 - Combine the binary strings:
01111100 - Regroup in sets of three from the right:
[001] [111] [100](padded with a leading zero) - Convert 3-bit binary to octal:
001 ➔ 1,111 ➔ 7,100 ➔ 4 - Combined Result: 174₈
Example 2: Convert Hex A3 to Octal
- Convert hex to 4-bit binary:
A ➔ 1010,3 ➔ 0011 - Combine binary:
10100011 - Regroup in sets of three from the right:
[010] [100] [011](padded with a leading zero) - Convert to octal:
010 ➔ 2,100 ➔ 4,011 ➔ 3 - Combined Result: 243₈
Frequently Asked Questions
Can I convert hex directly to octal without binary? ▼
You can convert the hexadecimal number to decimal first (base-10), and then perform repeated division by 8 to convert the decimal number to octal. However, for most developers, converting through binary is much faster and less prone to math errors.
What is the octal value of hex FF? ▼
The hex value FF represented in binary is 11111111. Grouped into sets of 3, it becomes: 011 (3), 111 (7), and 111 (7). Thus, FF₁₆ = 377₈.
Binary to Hex Mapping
| Hex | 4-Bit Bin | Hex | 4-Bit Bin |
|---|---|---|---|
| 0 | 0000 | 8 | 1000 |
| 1 | 0001 | 9 | 1001 |
| 2 | 0010 | A | 1010 |
| 3 | 0011 | B | 1011 |
| 4 | 0100 | C | 1100 |
| 5 | 0101 | D | 1101 |
| 6 | 0110 | E | 1110 |
| 7 | 0111 | F | 1111 |