Octal to Hex Converter: How to Convert Base 8 to 16
Understand how to convert octal values to hexadecimal step-by-step using intermediate binary groupings.
Try it: Octal to Hex mini-calculator
Intermediate binary conversion.
Octal (base-8) and hexadecimal (base-16) numbers are closely related because both bases are powers of 2. Specifically:
- Each octal character maps to exactly 3 binary digits (bits).
- Each hexadecimal character maps to exactly 4 binary digits (bits).
Therefore, the easiest way to perform the conversion by hand or in simple registers is to convert the octal digits to a combined binary representation and then regroup that binary string into sets of four.
Step-by-step conversion method.
- Convert each individual digit of the octal number into its 3-digit binary equivalent (e.g.
2 ➔ 010). - Combine all the 3-bit binary groups into a single binary string.
- Regroup the binary string into sets of four bits starting from the rightmost bit. If the leftmost group has fewer than four bits, pad it with leading zeros.
- Convert each 4-bit binary group to its corresponding hexadecimal digit (0-9, A-F).
Conversion examples.
Example 1: Convert Octal 174 to Hex
- Convert octal digits to 3-bit binary groups:
1 ➔ 001,7 ➔ 111,4 ➔ 100 - Combine the binary strings:
001111100 - Regroup in sets of four from the right:
[0111] [1100](dropping leading zeros) - Convert 4-bit groups to hexadecimal:
0111 ➔ 7,1100 ➔ C - Result: 7C₁₆
Example 2: Convert Octal 267 to Hex
- Convert octal to 3-bit binary:
2 ➔ 010,6 ➔ 110,7 ➔ 111 - Combine binary:
010110111 - Regroup in sets of four from the right:
[1011] [0111](dropping leading zero) - Convert to hex:
1011 ➔ B,0111 ➔ 7 - Result: B7₁₆
Frequently Asked Questions
How is octal converted to hex using decimal? ▼
You can convert the octal number to decimal by multiplying each digit by its power of 8 (starting with 8⁰ on the right) and summing the products. Once in decimal, perform repeated division by 16 to find the hexadecimal equivalent. This is another popular method when not using binary.
What is octal 77 in hexadecimal? ▼
Octal 77 in binary is 111111. Regrouping as 4-bit sets starting from the right gives 0011 (3) and 1111 (F), yielding the hexadecimal value 3F₁₆.
Octal to Binary Mapping
| Octal | 3-Bit Bin | Octal | 3-Bit Bin |
|---|---|---|---|
| 0 | 000 | 4 | 100 |
| 1 | 001 | 5 | 101 |
| 2 | 010 | 6 | 110 |
| 3 | 011 | 7 | 111 |