Binary to octal converter

What is the binary number system?

The binary number system is a base-2 numeral system widely used in computer science and digital electronics. It uses only two digits — 0 and 1 — to represent values.
Each digit in a binary number corresponds to a power of 2. The rightmost bit represents $2^0$, the next one to the left represents $2^1$, and so on.

For example:

Binary numbers are commonly used because electronic circuits can easily distinguish between two states — ON (1) and OFF (0).

What is the octal number system?

The octal number system is a base-8 numeral system that uses digits from 0 to 7. It’s a compact way to express binary numbers and was historically used in early computers that operated on 12, 24, or 36-bit words.

Each digit in an octal value corresponds to three binary digits (bits) because $2^3 = 8$. Hence, converting between binary and octal is straightforward and does not require intermediate conversion to decimal.

For example:

Step-by-step conversion

Step 1: Convert binary to decimal

Step 2: Decimal to octal

We repeatedly divide the number by 8 and record remainders.

Reading remainders from bottom to top gives $326_8$.

Convert with binary grouping

Each octal digit represents 3 binary bits.

For example, to convert $100110011_2$ to octal, group into sets of three: $100\ 110\ 011$.
Convert each group:
$100_2=4_8$, $110_2=6_8$, $011_2=3_8$.
Thus $100110011_2 = 463_8$.

You can use both methods to convert binary to octal - using decimal as an intermediate step or directly grouping into 3-bit sets.

Frequently asked questions

How to convert binary 100110011 to octal manually?

Group into sets of three: $100\ 110\ 011$.
Convert each group:
$100_2=4_8$, $110_2=6_8$, $011_2=3_8$.
Thus $100110011_2 = 463_8$.

Why does grouping by three binary digits work perfectly?

Because $2^3=8$, three binary digits correspond exactly to one octal digit, making conversion direct and error-free.

How to verify binary-to-octal conversion accuracy?

Convert binary to decimal, then decimal to octal using division by 8. If both octal values match, your conversion is correct.

What is the octal equivalent of binary 11111111?

Let’s convert binary 11111111 to decimal, then decimal to octal.

Then convert 255 to octal:

Thus, the octal equivalent of binary 11111111 is 377.