Binary to Octal Converter

To use this binary to octal conversion tool, you must type a binary value like 11011011 into the left field below and hit the Convert button. The converter will give you the octal equivalent of the given binary.

Binary Value Convert

Octal Value swap conversion: Octal To Binary Converter

Binary to octal conversion result in base numbers

Binary System

The binary numeral system uses the number 2 as its base (radix). As a base-2 numeral system, it consists of only two numbers: 0 and 1. 

While it has been applied in ancient Egypt, China and India for different purposes, the binary system has become the language of electronics and computers in the modern world. This is the most efficient system to detect an electric signal’s off (0) and on (1) state. It is also the basis for binary code that is used to compose data in computer-based machines. Even the digital text that you are reading right now consists of binary numbers.

Reading a binary number is easier than it looks: This is a positional system; therefore, every digit in a binary number is raised to the powers of 2, starting from the rightmost with 2⁰. In the binary system, each binary digit refers to 1 bit.

The Octal System

The octal number system (or shortly oct) uses the number 8 as its base (radix). As a base-8 numeral system, it uses eight symbols: The numbers from 0 to 7, namely 0, 1, 2, 3, 4, 5, 6 and 7. Although it was used by some native American tribes until the 20th century, the octal system has become popular in the early ages of computing as a language of computer programming. This is because the octal system shortens binary by simplifying long and complex chains of binary displays used by computers.

The octal system is mainly used for counting binary in groups of three: Each octal digit represents three binary digits. Since 8 is 2 to the third power (2³), the octal system became a perfect abbreviation of binary for machines that employ word sizes divisible by three - which were 6-bit, 12-bit, 24-bit or 36-bit. Nowadays, most modern systems use hexadecimal rather than octal. However, octal numbers are an important part of basic knowledge in electronics.

How to Convert Binary to Octal

Converting from binary to octal is very easy since octal numbers are only simplified versions of binary strings. You just need to remember that each octal digit represents three binary digits so that three binary digits will give only one octal digit. While the method is quite easier than it sounds, it’s always useful to use a binary to octal conversion chart to save time.

• Step 1: Write down the binary number and group the 0’s and 1’s in sets of three. Start doing this from the right. If the leftmost group doesn’t have enough digits to make up a set of three, add extra 0’s to make another group.
• Step 2: Write 4, 2 and 1 below each group. These are the weights that the positions carry (2²,2¹,2⁰).
• Step 3: Every group of three in binary will give you one digit in octal. Multiply the 4, 2 and 1’s by the digit above.
• Step 4: Add the products within each set of three. Write the sums below the groups they belong to.
• Step 5: The digits you get from the sums in each group will give you the octal number, from left to right.

Now, let’s apply these steps to, for example, the binary number (111010)₂

Step 1: 111010 has six digits and therefore can be grouped in sets of three without adding 0’s. 
Think of the number as (111)(010).

Step 2: Write 4, 2 and 1 below each group.
        111	010
        421	421

Step 3: Multiply the 4, 2 and 1’s with the digit above.
        111	010
        421	421
        421	020

Step 4: Add the products within each set of three.
In the first group, 4 + 2 + 1 = 7
In the second group, 0 + 2 + 0 = 2
Write these digits below the groups they belong to.
        111	010
        421	421
        421	020
        7         2

Step 5: (111010)2  = (72)8

Binary to Octal Conversion Examples

Example 1: (1010001)₂ = (121)₈

(1)(010)(001)
(Notice that the digits in this binary number cannot be grouped all in three. 
Add two 0’s and repeat the above explained steps.)

	001	010	001
	421	421	421
	001	020	001
	1	 2	 1

Example 2: (10100101.01)₂ = (245.2)₈

(Notice that this binary number has a decimal point. 
It also cannot be automatically grouped in sets of three. 
You need to add 0’s both the leftmost and the rightmost parts.)

	010	100	101.	010
	421	421	421.	421
	020	400	401.	020
	2	4	5.	2
        

Related converters:
Octal To Binary Converter

Binary Octal Conversion Chart Table

© 2009-2024 www.BinaryHexConverter.com | Privacy Policy | Contact Us | @BinHexConverter