Octal number system
The octal number system is a positional numeral system that uses a base of 8. It is often used in computing, especially in early computer systems and programming languages. In the octal system, digits range from 0 to 7, and each digit’s position represents a power of 8.
Octal numbers are commonly used to represent binary numbers because every three bits in binary can be represented by one octal digit. Each octal digit corresponds to a unique combination of three binary digits (bits). Here’s a table that shows the mapping between binary and octal digits:
| Binary | Octal |
|---|---|
| 000 | 0 |
| 001 | 1 |
| 010 | 2 |
| 011 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
For example, the octal number 7532 is equivalent to the binary number 111 101 011 010. To convert an octal number to its decimal equivalent, you can multiply each digit by 8 raised to the power of its position and sum up the results.
However, it’s worth noting that octal representation is not as commonly used today in modern computing systems. Hexadecimal (base 16) is more prevalent due to its convenient mapping to binary and its use in representing memory addresses and binary data.
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