Convert octal numbers to decimal with a step-by-step positional breakdown showing each digit weight and running total.
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Number Systems
The octal to decimal converter translates octal (base-8) numbers into their decimal (base-10) equivalents. Enter an octal value and see the decimal result with a positional breakdown.
Multiply each octal digit by 8 raised to its position index (starting from 0 on the right) and sum all the products to obtain the decimal value.
For example, octal 144 equals 1 times 64 plus 4 times 8 plus 4 times 1, giving decimal 100.
decimal = sum of (digit_i * 8^i)
Each octal digit is multiplied by 8 raised to its position, starting from 0 on the right.
Octal-to-decimal conversion helps verify Unix permission values, interpret legacy octal constants in C source code, and understand historical computing documentation that used octal notation.
Frequently asked questions
Octal 777 equals 7 times 64 plus 7 times 8 plus 7 times 1 = 511 in decimal.
Many early machines had word lengths divisible by 3 (such as 12, 18, or 36 bits), making octal a natural compact notation for binary data.
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