Binary to Octal Conversion

Binary and Octal number systems are used to write numbers using different rules as compared to the decimal number system. In the binary number system, we use only 0 and 1 digits to write numbers, while in the octal number system we use 0 to 7 digits to write numbers. Every number written in one number system can be converted to another, by applying some set of rules.

In mathematics, we have learned about the different types of numbers such as rational numbers, real numbers, whole numbers, natural numbers, etc. In the digital world, numbers are used a little differently through the number system. There are mainly 4 types of the number system that are commonly used:

• Octal Number System which has a base of 8 and is represented as \((n)_{8}\)
• Binary Number System which has a base of 2 and is represented as \((n)_{2}\)
• Decimal Number System which has a base of 10 and is represented as \((n)_{10}\)
• Hexadecimal Number System which has a base of 16 and is represented as \((n)_{16}\)

In this article, we are going to learn about binary to octal conversion. Let's begin!

The binary number system is closely associated with the computer system where numbers 0 and 1 are only used. Binary numbers deal with the base 2 along with digits 0 and 1 only. This number system does not deal with other numbers such as 2,3,4,5 and so on. Each digit i.e. either 0 or 1 is referred to as a bit in the binary number system. For example, \((01101)_{2}\), \((01000010)_{2}\), \((11000101)_{2}\) are a few binary numbers.

The octal number system deals with digits from 0 to 7 along with a base of 8. Numbers like 8 and 9 are not included in the octal number system. Just as the binary, octal number system is used in minicomputers but with digits from 0 to 7. For example, \((76)_{8}\), \((121)_{8}\), \((350)_{8}\) are a few octal numbers.

Since binary numbers are used in computers in the form of bits or bytes and octal numbers are used in electronics, direct conversion from binary to octal is not a method. There are two kinds of methods that are used in the binary to octal conversion. 

Method 1: Converting Binary to Decimal then from Decimal to Octal 

Here are the steps that need to be followed for this method. 

• Step 1: Identify the binary number
• Step 2: Convert binary to decimal by multiplying each digit by 2^n-1 where 'n' is the position of the digit from the right.
• Step 3: The derived answer is the decimal number for the given binary number
• Step 4: Divide the decimal number by 8
• Step 5: Note the remainder
• Step 6: Continue the above two steps with the quotient till the quotient is zero
• Step 7: Write the remainder in the reverse order
• Step 8: The answer is the required octal number for the binary number

For example: Convert the binary number \((1011101)_{2}\) to an octal number. 

Solution: According to method 1, first convert the binary number to decimal number. 

 \((1011101)_{2}\) =  ( 1 x 2⁶) + (0 x 2⁵) + (1 x 2⁴) + (1 x 2³) + (1 x 2²) + (0 x 2¹) + (1 x 2⁰)

                     =  64 + 0 + 16 + 8 + 4 + 0 + 1

                    = 93

 \((1011101)_{2}\) = \((93)_{10}\)

The next step is to convert the decimal number to an octal number by dividing 93 by 8. 

93 divided by 8 will give 5 as remainder and 11 as the quotient

11 divided by 8 will give 3 as remainder and 1 as the quotient

1 divided by 8 will give 1 as remainder and 0 as the quotient

Collect the remainders in reverse order we get 1 3 5

Therefore, binary number \((1011101)_{2}\) = \((135)_{8}\)

Method 2: Converting Binary to Octal by grouping 

Here are the steps that need to be followed for this method.

• Step 1: Identify the binary number i.e. the digits should be either 0 or 1 with base 2.
• Step 2: Group all the 0 to 1 in a set of three starting from the right side.
• Step 3: Add 0's to the left if it does not form a group of three. Each group must have three digits.
• Step 4: Look at the binary to octal conversion table to get the accurate numbers.
• Step 5: Once obtained, that number is the octal number  

For example: Convert the binary number \((01110101)_{2}\) to an octal number.

Solution: Using the grouping method, set the binary number into three numbers in each group. 

\((01110101)_{2}\) = 001 110 101 = 1 6 5 

\((01110101)_{2}\) = \((165)_{8}\)

Binary to Octal Conversion Related Articles

Here is a list of topics that are related to the binary to octal conversion. Click to know more!

• Long Division 
• Division 
• Addition 
• Remainder
• Base 
• Convert 22 in Binary
• Convert 16 in Binary
• Convert 255 in Binary 
• Convert 128 in Binary 
• Binary Number System
• Binary Subtraction
• Binary to Decimal Formula
• Decimal to Binary Formula  
• Binary to Decimal Calculator
• Decimal to Binary Calculator

What is Binary Number System?

The binary numbers are associated with the digital world where numbers only numbers 0 and 1 are used with base 2 and do not deal with other numbers such as 2,3, 4,5, etc. The numbers 0 and 1 are referred to as a bit in the binary number system. For example: \((01110001)_{2}\), \((011010101)_{2}\), \((0101011)_{2}\) are a few binary numbers.

What is Octal Number System?

Like the binary number, octal numbers are also used in the digital world but it deals with numbers from 0 to 7 only with a base of 8. Numbers from 8 and beyond are not included in the octal number system and are also counted in bits. Octal numbers can be converted to binary numbers by finding the octal equivalent of the binary number from the conversion table. For example: \((350)_{8}\),  \((570)_{8}\),  \((35)_{8}\) are a few octal numbers.

What are the Methods used in Conversion of Binary to Octal Number System?

There are two different methods used in the conversion of binary to octal numbers, they are:

• Method 1: Converting Binary to Decimal then from Decimal to Octal - Where the binary number needs to be converted to the decimal number and that decimal number will be converted to the octal number. 
• Method 2: Converting Binary to Octal by grouping - Where the binary number is grouped into the set of threes. The number is obtained by looking at the conversion table. 

What are the 4 Types of Number Systems?

The four different types of number system are:

• Octal Number System which has a base of 8 and is represented as \((n)_{8}\)
• Binary Number System which has a base of 2 and is represented as \((n)_{2}\)
• Decimal Number System which has a base of 10 and is represented as \((n)_{10}\)
• Hexadecimal Number System which has a base of 16 and is represented as \((n)_{16}\)

What is the Base of the Binary Number?

The base of the binary number is base 2 and when converted to the octal number the base changes to base 8. 

How do you Convert Binary to Octal?

The conversion from binary to octal numbers has two methods. The first method is where the binary number has to be converted to a decimal number which is then converted to the octal number. The second method of converting binary to octal numbers is done directly by using the conversion table.

What is the Octal Equivalent of the Binary Number?

As the octal number system uses only eight digits from 0 through 7 there are no numbers or letters used for 8 and above 8. For the conversion of octal to binary and vice versa, every 3 binary digit represents one octal number and vice versa. Hence, octal equivalents can be derived from binary numbers by grouping consecutive binary digits into groups of three (starting from the right). Below mentioned is the binary to octal conversion table:

What is the Octal Equivalent of the Binary Number 1011 1101?

The first step is to divide the binary number into parts with three numbers each. Hence,  the number 1011 1101 = 010 111 101 = 2 7 5. Therefore,  \((1011 1101)_{2}\) = \((275)_{8}\).