For converting octal to binary numbers, we have some steps by which we can convert them. Let us study both systems and their conversion.

Octal Numbers: The numbers which have a base of 8 are known as Octal numbers. We can represent them as N8. This number system uses 0,1,2,3,4,5,6 and 7 to represent numbers.

For Example, 2128, 5698, 6548, etc.

Binary Numbers: The numbers which are having base 2 are known as Binary numbers. We can represent them as N2 . This system uses only 0 and 1 to represent digits. This is the language of machines like a computer. Our computers read the data only in binary form.

For Example, 1012 , 1101112, 1110002, etc.

Steps to convert Octal to Binary

We cannot convert octal numbers directly into binary, we have to follow a two steps process for converting them.

OCTAL DECIMAL BINARY

First Process is to convert octal numbers into decimals then we will convert them into binary.

• Steps To Convert Octal to Decimal

1. In the first step, count the number of digits that are given in octal numbers. Let us say, n digits are present in an octal number.
2. Then, multiply each digit of the octal number by 8n-1, while the digit is inside the nth place from the right side of the number. If the number has a decimal component, multiply each digit in the decimal part through 8-m, when the digit is at the mth place from the decimal point.
3. Now, you have to add all terms after multiplication.
4. Here, you have the required decimal number.

• Steps To Convert Decimal to Binary

1. In the very first step of the second process, you have to divide the decimal number by 2.
2. Now, write the remainder obtained after division.
3. Repeat the above two steps, till you get the zero quotients.
4. Reverse the remainder and write it.
5. Here, you get the required binary number which is equivalent to the given octal number.

Examples

1. Convert 258 octal numbers to binary numbers.

Sol. Number of digits in Octal Number, n = 2

258 = (2 × 81) + (5 × 80)

      = 2 × 8 + 5 × 1

      = 16 + 5

      = 21

21 is the equivalent decimal number to the given octal number.

2nd Process, To convert decimal number into binary number

We will make a table that makes our conversion process easy.

Hence, the equivalent binary number is 101012.

⇒258 = 101012

1. Convert 538 octal numbers to binary numbers.

Sol. Same as the above process, firstly we have to convert this octal number into a decimal number, so let’s do it.

538 = (5 × 81) + (3 × 80)

    =  5 × 8 + 3 × 1

      = 40 + 3

      = 43

43 is the equivalent decimal number of given octal number.

Now, we will convert this obtained number into binary.

The next step is to reverse the order of remainders, in the above question we have the same digits from both sides so we did not feel the necessity of reversing, that’s why this step is not highlighted there. But here it is necessary, that’s why we have to take care of this step.

Hence, the equivalent binary number is 1010112. 

⇒538 = 1010112 

Let’s do a three-digit octal number conversion.

1. Convert 2008 into a binary number.

Sol. n = 3

2008 = (2 × 82) + (0 × 81) + (0 × 80)

          = 2 × 64 + 0

= 128

128 is the equivalent decimal number.

Now, let us proceed for decimal to binary conversion.

100000002 is the equivalent binary number.

⇒2008 = 100000002

Octal To Binary Conversion Table

We can use this table for octal to binary conversion, which makes our work so easy.

Let us solve the above question with the help of this table.

Ques. Convert 538 to a binary number.

Sol. By using table, we can convert as

538 = (101 011)2

This is the same answer obtained above, so we can also convert it directly without using the long two-step process.

Conclusion-

As you may know that computers can understand only binary language, not our language, that’s why knowing Binary language is important for us to some extent. And, the Octal number system is commonly used as a shorter representation of binary numbers. So, learning about their conversion is also necessary.