Octal to Binary Converter

How to convert octal to binary?

To convert an octal number to binary, you simply translate each octal digit into its corresponding 3-bit binary representation. Because the base of octal is $8$ ($2^3$), each individual octal digit maps perfectly to a group of three binary digits.

The Conversion Table

Use this reference to map each octal digit (0–7) to its 3-bit binary equivalent:

Octal Digit	Binary (3-bit)
0	000
1	001
2	010
3	011
4	100
5	101
6	110
7	111

Step-by-Step Method

1. Separate2222 the octal number into individual digits.

2. Convert each digit into its 3-bit binary group using the table above.

3. Concatenate (combine) the binary groups in the same order to form the final result.

Example: Convert $527_8$ to Binary

• Step 1: Break down $527$: $5$ | $2$ | $7$

• Step 2: Convert to 3-bit binary groups:

  • $5 \rightarrow 101$

  • $2 \rightarrow 010$

  • $7 \rightarrow 111$

• Step 3: Join them together: $101010111$

Therefore, $527_8 = 101010111_2$.

Note: You can remove leading zeros if they appear at the very beginning of the final binary string, as they do not change the value. However, keep internal zeros (like the $010$ in the example above) exactly as they are.