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In the field of computer programming and digital electronics, hexadecimal (base 16) and octal (base 8) are often used for numerical representation.
If you need to convert a hexadecimal number to an octal, the process involves converting each hexadecimal digit into four binary digits and then grouping the binary digits into groups of three to obtain the corresponding octal digit.
In this guide, we’ll provide step-by-step instructions on how to convert hexadecimal to octal, along with an example and reference tables.
To convert a hexadecimal number to an octal, follow these steps:
| Hexadecimal (base 16) | Binary (base 2) |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
| A | 1010 |
| B | 1011 |
| C | 1100 |
| D | 1101 |
| E | 1110 |
| F | 1111 |
Group the binary digits into groups of three, starting from the least significant digit.
Convert every group of three binary digits into one octal digit using the table below.
| Binary (base 2) | Octal (base 8) |
|---|---|
| 000 | 0 |
| 001 | 1 |
| 010 | 2 |
| 011 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
Example: Converting Hexadecimal 6C16 to Octal
| Hexadecimal (base 16) | Binary (base 2) |
|---|---|
| 6 | 0110 |
| C | 1100 |
Therefore, 6C16 in hexadecimal is equivalent to 0110110011002 in binary.
| Binary (base 2) | Binary Grouping | Octal (base 8) |
|---|---|---|
| 0110 | 110 | 6 |
| 1100 | 011 | 3 |
| 0100 | 100 | 4 |
Therefore, 0110110011002 in binary is equivalent to 1548 in Octal digits.
Use the following reference tables to help you with your hexadecimal to octal conversions:
| Hexadecimal (base 16) | Binary (base 2) |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
| A | 1010 |
| B | 1011 |
| C | 1100 |
| D | 1101 |
| E | 1110 |
| F | 1111 |
| Binary (base 2) | Octal (base 8) |
|---|---|
| 000 | 0 |
| 001 | 1 |
| 010 | 2 |
| 011 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
Converting hexadecimal to octal involves converting each hexadecimal digit to four binary digits and then grouping the binary digits into groups of three to obtain the corresponding octal digit. Remember to use the reference tables provided to help you with your conversions.
With these steps and tables, you can easily convert hexadecimal to octal, which is useful in digital electronics and computer programming.