Binary to Octal Conversion

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In binary to octal conversion, we learn to convert base 2 number system into base 8 number system. We cannot directly convert binary to octal, so we first convert binary to decimal, then the decimal number to the equivalent octal number system. Binary numbers are commonly used in computers, in the form of bits and bytes, since the computer understand the language of 0 and 1 only. At the same time, octal numbers are used in electronics. Before going to the conversion, we have to learn about octal and binary numbers.

What are Binary Numbers?

Numbers to base 2 is called binary numbers. It uses only two digits, 0 and 1. It is denoted by a₂, where a is a number with 0’s and 1’s.

Examples:

111110₂
1111111₂
1011001₂

What are Octal numbers?

The number to the base 8 is called octal numbers. It uses the numbers from 0 to 7. The numbers 8 and 9 are not included in the octal number system. It is denoted by a₈ where a is a number with digits 0 to 7.

Examples:

2145₈
7165₈
46₈

Conversion from Binary to Octal

In number system, you will come across different types of numbers such as binary, octal, decimal and hexadecimal. To convert binary numbers to octal numbers, follow the below steps:

Take the given binary number
Multiply each digit by 2^n-1 where n is the position of the digit from the decimal
The resultant is the equivalent decimal number for the given binary number
Divide the decimal number by 8
Note the remainder
Continue the above two steps with the quotient till the quotient is zero
Write the remainder in the reverse order
The resultant is the required octal number for the given binary number

Also read:

Number System Conversion
Convert Octal To Binary
Convert Decimal To Octal

Here is a table for decimal number and equivalent octal number, to solve the problems based on their conversion more quickly.

Decimal Number	Octal Number
0	0
1	01
2	010
3	011
4	100
5	101
6	110
7	111

Binary to Octal conversion Examples

Example 1: Convert 1010101₂ to octal

Solution:

Given binary number is 1010101₂

First, we convert given binary to decimal

1010101₂= (1 * 2⁶) + (0 * 2⁵) + (1 * 2⁴) + (0 * 2³) + (1 * 2²) + (0 * 2¹) + (1 * 2⁰)

= 64 + 0 + 16 + 0 + 4 + 0 + 1

= 64 + 21

010101₂= 85 (Decimal form)

Now we will convert this decimal to octal form

Therefore, the equivalent octal number is 125₈.

Example 2: Convert 01101₂ to octal

Solution:

Given binary number is 01101₂

First we convert given binary to decimal

01101₂= (0 * 2⁴) + (1 * 2³) + (1 * 2³) + (0 * 2) + (1 *2⁰)

= 0 + 8 + 4 + 0 +1

01101₂= 13 (Decimal form)

Now we will convert this decimal to octal form

Therefore, the equivalent octal number is 15₈.