In order to convert octal to binary number, we have to follow a few steps. Octal numbers have base 8 and binary numbers have base 2. We can convert the octal number into decimal and then convert the decimal number into its equivalent binary number. Also, we can remember the octal to the binary equivalent table to do the quick conversion. Before we learn the conversion method, let us learn about both the number systems.

Octal Numbers: Octal numbers are the numbers which have base 8. It is represented as N₈. It uses the digits 0,1, 2, 3, 4, 5, 6 and 7 to represent the numbers in this number system. For example:

• 112₈
• 1008₈
• 789₈, etc.

Binary Numbers: Binary numbers have base 2 and are represented by two digits, i.e. 0 and 1. They are the combination of binary digits, 0’s and 1’s. These numbers have wide application in the computer system to store data. For example:

• 0011₂
• 111101₂
• 101010₂

How to Convert Octal To Binary?

Conversion of octal to binary number is a two-step process. First, we need to convert the given octal number into its equivalent decimal number and then convert the decimal into binary. Let us learn the complete steps here.

Octal to Decimal Conversion

• Count the number of digits present in the given number. Let the number of digits be ‘n’.
• Now multiply each digit of the number with 8^n-1, when the digit is in the nth position from the right end of the number. If the number has a decimal part, multiply each digit in the decimal part by `8<sup>-m</sup>` when the digit is in the m^th position from the decimal point.
• Add all the terms after multiplication.
• The obtained value is the equivalent decimal number.

Decimal to Binary Conversion

• Take the above-produced decimal number and divide it by 2.
• Note down the remainder.
• Continue the above two steps for the quotient till the quotient is zero.
• Write the remainder in the reverse order.
• The received number is the equivalent binary number for the given octal number.

Also, see:

Solved Examples

Q.1: Convert 41₈ to a binary number.

Solution: Given number is 41₈

41₈ = (4 * 8¹) + (1 * 8⁰)

= 4 * 8 + 1 * 1

= 32+1

= 33(Decimal number)

Now convert this decimal number into its equivalent binary number. Let us draw a table to show the conversion of decimal to binary as given below.

Therefore, the equivalent binary number is 100001₂.

Hence, 41₈ = 100001₂

Q.2: Convert 10₈ to a binary number.

Solution: Given number is 10₈

10₈ = (1 * 8¹) + (0 * 8⁰)

= 1 * 8 + 0 * 1

= 8 + 0

= 8 (Decimal number)

Now convert this decimal number into its equivalent binary number. Let us draw a table to show the conversion of decimal to binary as given below.

Therefore, the equivalent binary number is 1000₂.

Hence, 10₈ = 1000₂

Convert Octal to Binary Using Table

We can also use the octal number table to convert a number with base 8 to a number with base 2. Using this table we can also convert a binary number to an octal number. First, let us write the table.

Example: Convert 12₈ into a binary number.

Solution: Given, 12₈ is the octal number.

Now with the help of the table, we can write;

12₈ = (001 010)₂

Since zeros on the left, most of digit 1 does not have any significance. Thus,

12₈ = (1010)₂

Practice Questions

1. Convert 122₈ into binary number.
2. Convert the octal number 200₈ into its equivalent binary number.
3. Convert (98)₈ to a binary number.