Octal to Binary Converter

Going the other way? Convert binary back to octal →

How do you convert octal to binary?

Octal to binary conversion works in groups of 3 bits, because one octal digit is worth exactly 3 bits, so no arithmetic is needed.

1. Take the first octal digit.
2. Write it as 3 binary digits from the table.
3. Repeat for every digit, keeping the order.
4. Join the groups and drop any leading zeros: 472 = 100111010.

Octal to Binary Conversion Table

One hexadecimal digit equals exactly 4 bits (16 = 2⁴); one octal digit equals exactly 3 bits (8 = 2³). Hex and octal are therefore converted by grouping bits, and hex ↔ octal passes through binary. That is the whole method, so the table below is the only thing you need: every group of 3 bits has exactly one octal digit, and the mapping never changes. Binary writes values on the digit set 0, 1 with each place worth 2ⁿ, and a value marked 0b is binary; octal values are marked 0o.

Each base is defined by three things: which digits it uses, how a value is marked, and what each position is worth.

Worked Example: 472 to Binary

One value, converted the long way so the working is visible. This is the same grid the converter shows when you turn on "show steps".

Both bases here are powers of two, so no division is needed. One octal digit is worth exactly 3 bits, which means the conversion is a regrouping of the same bits rather than a change of value.

Written out, 472 is 100111010 in binary. Regrouping those bits into 3s from the right, and padding the leftmost group with zeros if it is short, gives 100111010. Counting the groups from the left instead is where this goes wrong: the padding then lands on the wrong end and every digit shifts.

Check it in reverse

The value returns unchanged. Convert 100111010 back and you get 472, because a base change rewrites the digits without touching the quantity they stand for. That is the whole test: if the round trip differs, a digit was misread. To check it by hand, convert the octal result back to binary and compare it with the number you started from.

Worked examples: octal to binary

Each example gives the value first, then the working. Click a value to load it in the converter.

Every example above reverses exactly — run the same value the other way, binary to octal.

What About Padding, Fractions and Width?

Leading zeros and width

A number carries no leading zeros unless a width is fixed. 100111010 and 0100111010 are the same value, so the converter writes the short form. Fixed widths belong to bytes and registers, not to arithmetic. how any base converts to any other covers where width does matter.

Fractions and the point

Digits after a point convert by the same rule with negative powers, so the first place after the point is worth 1/2. Many fractions that end neatly in decimal repeat forever in binary, which is where rounding creeps in.

Negative values

A minus sign is kept in front of the digits. Fixed-width binary encodes sign differently, using two's complement, and that is a separate rule from the base change itself.

How large a value can be

The method has no ceiling; each extra octal digit multiplies the range by 8. Practical limits come from the width a machine stores the value in, not from the conversion.

Octal to Binary in Code

The same rule in one line. Both group the bits and return the binary digits.

Python: format(int('472', 8), 'b')

JavaScript: parseInt('472', 8).toString(2)

Common Mistakes

• Reading the remainders top to bottom. They come out in reverse, so the digits land backwards.
• Using a digit the base does not have — an 8 in octal, or a 2 in binary. The value cannot be read at all.
• Grouping bits from the left. Groups are counted from the right, and the leftmost group is the one that gets padded.
• Treating the result as a character code. 101 is a number here, not the letter A.

Frequently Asked Questions

Related Conversions

• Octal also converts to hex by the same route — octal to hexa conversion via binary.
• Octal also converts to decimal by the same route — octal to decimal calculator with the working shown.
• Octal also converts to text by the same route — octal escape codes to characters.
• If your input is text rather than octal, convert text to binary instead.
• If your input is decimal rather than octal, convert decimal to binary instead.
• If your input is hex rather than octal, convert hexadecimal to decimal instead.

The rest of the family sits on the rest of the binary converters in this family.