Octal to Binary Converter

To use this octal to binary conversion tool, you must type an octal value like 5432 into the left field below and hit the Convert button. The converter will give you the binary equivalent of the given octal.

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Octal to binary conversion result in base numbers

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.

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.

How to Convert Octal to Binary

Converting from octal to binary has a very straightforward method because octal numbers are shortened versions of binary strings. Remember that each octal digit represents three binary digits. Therefore, one octal digit should give three binary digits (bits). While octal can be converted to binary indirectly (first the to the decimal, then to binary), a direct method to convert octal to binary with steps is as follows:

• Step 1: Write down the octal number separating the digits. Each octal digit represents three binary digits and therefore is equal to a power of 2. The rightmost digit equals to 2⁰ (1), the next one equals to 2¹ (2) and the leftmost one equals to 2² (4). Write these numbers (4, 2 and 1) below the octal digits.
• Step 2: Determine which powers of two (4, 2 or 1) sum up to your octal digits. For example, if one of your octal numbers is 6, this means 4 and 2 sum up to 6 (and 1 is not used). If your octal number is 2, only 2 is used; 4 and 1 are not.
• Step 3: Write down 1 below those 4, 2 and 1’s that are used. Write down 0 below those that are not used.
• Step 4: Read 1’s and 0’s you just wrote from from left to right. You will get your binary number.

Let's apply these steps to the octal number (456)₈

Step 1: 
4	5	6
421	421	421

Step 2: 
4	5	6
421	421	421
(Notice the bold digits sum up to the octal value above. So the bold digits are 1 and the others are 0.)

Step 3: 
4	5	6
421	421	421
100	101	110

Step 4: (456)8 = (1010011100)2

Octal to Binary Conversion Examples

Example 1: (1234)8 = (001010011100)2
	1	2	3	4
	421	421	421	421
	421	421	421	421
	001	010	011	100

Example 2: (75426)8 = (111101100010110)2
	7	5	4	2	6
	421	421	421	421	421
	111	101	100	010	110

Example 3: (6574.73)8  = (110101111100.111011)2
	6	5	7	4.	7	3
	421	421	421	421.	421	421
	110	101	111	100.	111	011

Binary to Octal Converter

Octal to Binary Conversion Chart Table

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