🔂 Binary ↔ Octal Converter
Translate binary numbers into octal and octal back to binary with decimal equivalents.
Enter a binary or octal number to see its equivalent in the other base. Both directions display the decimal interpretation for validation.
Use digits 0 and 1 only. Negative sign is allowed.
Digits 0-7 only. Negative sign is allowed.
From Binary
Octal: 6453
Decimal: 3,371
From Octal
Binary: 110100101011
Decimal: 3,371
How to Use This Calculator
Enter binary or octal
Provide a binary number to see the octal form or an octal number to see binary output.
Check decimal value
Each conversion also shows the decimal equivalent for clarity and quick cross-referencing.
Copy the result
Use the outputs in software development, digital electronics, or academic exercises.
Formula
Octal digit = group of three binary bits (e.g. 101 → 5)
Binary = convert each octal digit into its 3-bit binary representation
Decimal conversions use base 2 or base 8 positional notation
Use the formula breakdown to confirm the calculation logic or perform the conversion manually if needed.
Full Description
Octal (base-8) represents binary groups of three bits, simplifying certain digital representations. This converter bridges binary and octal while also exposing the decimal value for general understanding.
It is useful in system programming, older Unix permissions, and legacy computing systems where octal shorthand is still common.
Negative numbers are supported by preserving the sign across conversions.
Frequently Asked Questions
Does it support fractional values?
This tool focuses on integers. For fractional conversions, handle integer and fraction parts separately.
Can I paste large numbers?
Yes, within JavaScript’s safe integer range. Very large numbers may lose precision.
Are uppercase/lowercase for octal digits relevant?
No. Octal digits are 0-7 only, so case is not applicable.
Is decimal output optional?
Decimal is always shown as a reference. It helps verify conversions and understand numeric magnitude.