Octal to Binary

An octal-to-binary conversion is done to convert an octal number (base 8) to its equivalent binary number (base 2). Here are the methods to convert an octal number to its binary counterpart.

Direct Method: Using Table

The octal number system has 8 digits from 0 to 7, represented in their equivalent binary using 3 bits.

Let us convert (363)₈ into its binary number.

Step 1: Grouping 363 into individual digits, we have 3, 6, and 3.

Step 2: Now, we find their corresponding binary numbers using the conversion table.

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

By converting each octal digit of (363)₈ to their binary numbers, we get

Octal Value	3	6	3
Binary Value	011	110	011

Here, we observe that each octal digit gives us a 3-bit binary number. Otherwise, we add zeros to maintain the correct number of digits.

Step 3: Taking the values from the first to last, (363)₈ equals (011110011)₂ or (11110011)₂.

For Fractional Octal Numbers

Similarly, we convert the fractional octal numbers into their corresponding binary. 

Now, converting (452.01)₈ to its equivalent binary, we get

For the Integral Part:

4 → 100, 5 → 101, and 2 → 010

For the Fractional Part:

0 → 000 and 1 → 001

Thus, (452.01)₈ = (100101010.000001)₂

Octal Value	5	3
Binary Value	101	011

Indirect Method: Without Using Table

There is another way by which each digit in any octal number is represented to its corresponding binary number without using the octal-to-binary conversion table.

Let us convert an octal number (73)₈ into its corresponding binary.

First, we convert 73 into a decimal number and then decimal to binary.

Step 1: Octal to Decimal

While converting (73)₈ to its decimal number, we multiply each digit from the right by the corresponding powers of 8, as shown.

Octal Value	7	3
Decimal Value	7 × 81	3 × 80

Now, on adding the values, we get the decimal number

(7 × 8¹) + (3 × 8⁰) = 56 + 3 = 59

Step 2: Decimal to Binary

Now, converting (59)₁₀ into its corresponding binary, we get

Thus, (73)₈ = (111011)₂.