Octal to Decimal
Convert base-8 octal strings into standard decimal values using powers of 8. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.
Enter valid octal digits (0 through 7 only).
Calculated Output
Step-by-Step Mathematical Proof
Active DerivationWhat Is Octal to Decimal?
Octal to decimal conversion evaluates a base-8 string into its base-10 numerical equivalent by expanding each digit with its power-of-eight weight.
How Does It Work?
Multiply each octal digit by 8^i, where i is its 0-indexed position from right to left, and sum the results.
Mathematical Algorithm
Step-by-Step Example
Important Rules & Edge Cases
- Digits 8 and 9 are strictly invalid in octal.
- The column weight increases by a factor of 8 for each position to the left.
Practical Applications in Engineering
- Decoding Unix file permission modes (e.g. converting mode 0777 to decimal 511).
- Interpreting aviation transponder radar squawk codes.
- Decompiling legacy mainframe binary dumps.
Common Mistakes to Avoid
- Caution: Treating the digits as base 10 directly.
- Caution: Including the digits 8 or 9 in input.
Frequently Asked Questions
What is octal 77 in decimal?
77 in octal is (7×8) + (7×1) = 56 + 7 = 63 in decimal.
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Convert octal numbers to hexadecimal format using binary as an intermediate grouping bridge.
Binary to Octal
Convert binary sequences into octal by grouping bits into 3-bit triplets from right to left.