Octal to Binary
In mathematics, there are different number systems to write numbers, say binary number system (base 2), octal number system (base 8), decimal (base 10), and hexadecimal number system (base 16). Octal to binary conversion is defined as converting a number from base8 to base2. It can be done in two ways that you will learn in this article. Let us move ahead and learn the conversion of octal to binary.
1.  What is Octal to Binary Conversion? 
2.  Octal to Binary Table 
3.  How to Convert Octal to Binary? 
4.  FAQs on Octal to Binary Conversion 
What is Octal to Binary Conversion?
Before learning about octal to binary conversion, let us quickly go through the meanings of the octal number system and binary number system. The binary number system uses only two digits 0 and 1 to represent numbers. It is also known as the base2 system. It is used with the computer system in which 0 and 1 digits are used to write various scripts. Each digit i.e. either 0 or 1 is referred to as a bit in the binary system. For example, (01101)_{2}, (01000010)_{2}, (11000101)_{2} are a few binary numbers. On the other hand, the octal number system includes digits from 0 to 7. Other digits like 8 and 9 are not included in this system. It is also known as the base8 system. Just as the binary, the octal number system is used in minicomputers. For example, (73)_{8}, (151)_{8}, (35)_{8} are a few octal numbers.
Conversion of octal to binary is defined as converting a number from base8 to base2 by using either direct or indirect methods. All the digits in an octal number are from the range of 0 to 7, while all the digits in a binary number include only 0 and 1. Let us observe the octal to binary table given in the next section.
Octal to Binary Table
Observe the octal to binary table given below which will help you to convert octal numbers to binary numbers. The octal to binary table shows the equivalent number of each octal digit to binary, for example, 0 in octal is equivalent to 000 in binary, 1 in octal is equivalent to 001 in binary, 2_{8} is the same as 010_{2}, and so on.
How to Convert Octal to Binary?
There are two ways to convert octal to binary, which are explained below:
 Convert octal to decimal and then decimal to binary
 The direct method of octal to binary conversion
Let us understand each method in detail one by one.
Method 1: Octal to decimal and then decimal to binary
In this method, we will first convert a number from octal to decimal (base 10), and then we will convert that decimal number to binary. To convert a number from octal to decimal, we multiply its digits starting from the right with 8 raised to exponents starting from 0 and then add the values. So, the first digit from the right will be multiplied by 8^{0}, which is equal to 1, the second digit will be multiplied by 8^{1} = 8, and so on.
Let us take an example of the number 56_{8}. The 8 written as the base represents that this is a base8 number. 56_{8} can be converted to base 10 as,
56_{8} = 6 × 8^{0} + 5 × 8^{1}
56_{8} = 6 × 1 + 5 × 8
= 6 + 40
= 46
Hence, 56_{8} = 46_{10}. Now, we will convert 46 which is a base 10 number to its binary equivalent. To convert decimal to binary, divide the given number by 2 and note down the quotient and reminder. Again divide the quotient obtained by 2, and note down the remainder. Repeat this process till you get 0 as the quotient. Write the remainders in order from right to left. Let us convert 46_{10} to binary.
Divide 46 by 2 ⇒ 46 ÷ 2 = Quotient  23, remainder  0
23 ÷ 2 = Quotient  11, remainder  1
11 ÷ 2 = Quotient  5, remainder  1
5 ÷ 2 = Q  2, R  1
2 ÷ 2 = Q  1, R  0
1 ÷ 2 = Q  0, R  1
Arrange all the remainders from right to left. We will get,
46_{10} = 101110_{2}
Therefore, we have converted an octal number 56_{8} to its binary equivalent 101110_{2}.
Method 2: Direct Method of Octal to Binary Conversion
Another method, surely an easier and less complicated one, is to directly convert a number from octal to binary by referring to the octal to binary table given above. In this method, we convert every digit of the given octal number to its binary equivalent by referring to the above chart. For example, using this method we can directly write 3_{8} as 011_{2}, 5_{8} as 101_{2}, etc.
Let us convert the same number 56_{8} from octal to binary using the direct method. There are two digits in this number, 5 and 6. Referring to the above octal to binary chart:
5_{8} → 101_{2}
6_{8} → 110_{2}
By combining these two, we will get, 56_{8} = 101110_{2}. Observe the image given below for your reference.
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Octal to Binary Examples

Example 1: Convert the octal number 72_{8} to a binary number using the decimal conversion method.
Solution: Given octal number 72_{8}. To convert it to a binary number using the decimal conversion method, we will first convert it to a decimal number.
⇒ 72_{8} = 2 × 8^{0} + 7 × 8^{1}
⇒ 72_{8} = 2 × 1 + 7 × 8
= 2 + 56
= 58_{10}
Now, we have to convert 58_{10} to a binary number by repeatedly dividing it by 2.
⇒ 58 ÷ 2 = Q  29, R  0
29 ÷ 2 = Q  14, R  1
14 ÷ 2 = Q  7, R  0
7 ÷ 2 = Q  3, R  1
3 ÷ 2 = Q  1, R  1
1 ÷ 2 = Q  0, R  1
We get, 58_{10} = 111010_{2}. Therefore, the octal to binary conversion of the number 72_{8} results in 111010_{2}.

Example 2: Change the octal number 35_{8} to its binary equivalent using the direct conversion method.
Solution: To convert an octal number to binary, we can use the octal to binary table with each of the given digits. The given number is 35_{8}. Referring to the table, we have,
3_{8} = 011_{2}
5_{8} = 101_{2}
By combining these binary bits, we get 35_{8} = 011101_{2}.

Example 3: How to convert 235_{8} octal to binary?
Solution: Let us convert the given number from octal to binary using the direct conversion method. The given number is 235_{8}.
2_{8} = 010_{2}
3_{8} = 011_{2}
5_{8} = 101_{2}
By combining these binary bits, we get 235_{8} = 010011101_{2}.
FAQs on Octal to Binary Conversion
What is Octal to Binary?
In mathematics, numbers can be written using different base systems like decimal, hexadecimal, binary, and octal number system. We can convert a number from one system to another by following some specific rules and procedures. Octal to binary is one such conversion in math. To convert a number from octal to binary system, we can use the octal to binary chart, or we can use the decimal method by first converting the given octal number to a decimal number followed by converting it to a binary number.
How do you Convert Octal to Binary?
To convert octal to binary, we can use any of the below two methods:
 Decimal conversion method
 Direct conversion
Any of the above methods can be used for the conversion. In the first one, we convert the given octal number to a decimal number by taking the sum of the products of each digit with a power of 8 starting from the right side. And then convert decimal to binary by dividing it by 2, followed by dividing the subsequent quotients by 2 in each step and noting down the remainders. Arrange the remainders in a reverse order to get the binary equivalent of the number. While in the direct conversion method, we refer to the octal to binary chart and directly write the binary bits of each of the digits in the given octal number.
How do you Convert 145 Octal to Binary?
145_{8} is equivalent to 01100101_{2}. To convert 145_{8} to a binary number, we will write the binary bits of each of its digits.
1 = 001_{2}
4 = 100_{2}
5 = 101_{2}
Therefore, 145_{8} = 001100101_{2} or 01100101_{2}.
How to Convert Octal to Binary Step by Step?
The stepbystep conversion of octal to binary is given below:
 Step 1: Convert the given octal number to its decimal equivalent.
 Step 2: Convert the obtained decimal number to the binary number.
By using these two steps, we can convert any octal number to its binary equivalent.
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