Octal to Binary Conversion

In this tutorial, you will learn about step by step method used for the conversion of octal to binary.

Octal & Binary Number

Octal number has its base as 8. That means it has total of 8 digits that are 0, 1, 2, ..., 6, 7. Whereas Binary number has its base as 2. That means it has total of 2 digits that are 0 and 1.

Octal to Binary Formula

To convert any octal number into binary, we have to convert each and every octal digit into the 3-bit binary number. Let’s take an example.

Convert the octal number, 364 to binary system. Or (364)8 = ( ? )2.

octal to binary conversion

From the above figure, we have 3 3-bit binary number, the first one is 011, the second one is 110, and the third one is 100. Therefore on combining, we have 011110100.

And the result is, (364)8 = (011110100)2.

Octal to Binary Conversion Table

Any octal number gets converted into binary number with the help of following table. You have to take octal digits and convert into its binary equivalent one by one. The table given below shows binary equivalent of all the 8 octal digits:

Octal Digit Equivalent Binary Value
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111

Octal to Binary Example

For example, let's suppose the number 254 is given as octal number, therefore to convert it into binary, you have to write binary equivalent of each octal digit one by one. The octal digits are 2, 5, and 4. Therefore, binary equivalent of 2, 5, and 4 octal digits are 010, 101, and 100 respectively. That is, (254)8 = (010101100)2

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