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See octal digits by base-8 position
755 → 493
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755
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Convert octal into decimal
Example: 755 → 493
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Understanding the Octal Number System
What Is Octal?
The octal number system, also called base-8, uses eight digits from 0 through 7 to represent values. Each digit position represents a power of eight: the rightmost digit is the ones place, the next is the eights place (8), then sixty-fours (64), five-hundred-and-twelves (512), and so on. Octal was once widely used in computing because early computers often used word sizes that were multiples of three bits, making octal a natural shorthand.
Octal in Modern Computing
Today, the most common use of octal is in Unix and Linux file permissions. The chmod 755 command uses three octal digits to set read (4), write (2), and execute (1) permissions for the owner, group, and others. The digit 7 means all permissions (4 + 2 + 1), 5 means read and execute (4 + 1), and 0 means no permissions. Understanding octal makes managing file permissions intuitive.
How Octal-to-Decimal Conversion Works
To convert an octal number to decimal, multiply each digit by its corresponding power of eight and add the results. For example, octal 755 equals (7 times 64) + (5 times 8) + (5 times 1) = 448 + 40 + 5 = 493. This positional calculation is the same principle used for any base conversion.
Historical Significance
The PDP-8, one of the most successful minicomputers ever made, used 12-bit words that were naturally expressed as four octal digits. Early programmers preferred octal over hexadecimal because each octal digit maps to exactly three binary bits, and 12 divides evenly by three but not by four. Some programming languages still support octal literals, where a number prefixed with 0 (like 0755) is interpreted as octal.