Octal to binary converter
Enter a octal number and get its binary value instantly, plus the other bases and the step-by-step working. Handles huge numbers, negatives and fractions.
Working for 7558
Each octal digit is exactly 3 bits, so you can convert group by group, no arithmetic needed:
How to convert octal to binary
- Replace every octal digit with its 3-bit pattern: 0 = 000 … 7 = 111.
- Join the groups and drop leading zeros.
- 755 = 111 101 101.
Octal survives mainly in Unix file permissions (chmod 755), in some older systems, and in C/Python literals such as 0o755. Binary is how hardware stores everything: bit flags, network masks, file permissions and machine code are all patterns of 1s and 0s.
See place value move
Every bit is worth twice the bit to its right. Flip the switches and watch the decimal, hex and octal values rebuild.
32 + 8 + 4 + 1 = 45 · hex 2D · octal 55
Related conversions
Binary to octal · Octal to decimal · Octal to hex · Decimal to binary · Hex to binary · any base 2–36 · signed (two's complement)
Questions people ask
How do you convert octal to binary?
Replace every octal digit with its 3-bit pattern: 0 = 000 … 7 = 111. Join the groups and drop leading zeros. 755 = 111 101 101.
What is 755 in binary?
755 in octal (base 8) is 111101101 in binary (base 2).
Does it handle negative numbers and fractions?
Yes. A leading minus sign is kept, and digits after a point are converted too. Some fractions that end in one base repeat forever in another (0.1 in decimal is 0.000110011… in binary), so the result is cut at 24 digits and marked as repeating.
Is there a size limit?
No practical one. The converter uses arbitrary-precision integers (JavaScript BigInt), so 64-bit, 128-bit and longer values convert exactly, without rounding.
Why is there no arithmetic in the working?
Every octal digit maps to a fixed group of bits, so conversion is a lookup rather than a calculation.