How to Convert Binary to Octal?

Are you looking for a simple way to convert binary numbers to octal numbers? If so, you have come to the right place! In this blog article, we will be discussing the basics of binary to octal conversion and provide a step-by-step guide to help you complete the process.

let's get started!

What are Binary numbers ?

Binary numbers are numbers that are expressed in base-2, meaning that they only contain two digits: 0 and 1. Binary numbers are used to represent data in computers, including digital images, sound, and text.

What are Octal number ?

Octal numbers are a type of number system that represent values using a base-8 system, which means there are 8 possible digits used for representing numbers (0-7).

How to convert binary to octal ?

There are two methods for converting a binary number to its octal equivalent.

We will discuss both of the methods

First method to convert Binary Number to octal

• Start by writing out the binary number.

• Group the binary number into sets of three from right to left.

• Replace each set of three with its octal equivalent.

• The result is the octal equivalent of the binary number.

Note: An extra '0' is put to the left of the binary number to make a complete group of 3 digits)

Example:

Binary: 10011111

Grouped: 010 011 111

Octal: 237

Let's understand by the help of below example

Note: To convert binary to octal we have to represent each digit as group of 3 as octal digit (0 to 7) i,e. (0 -> 000, 1 -> 001, 2 -> 010, ... 7 -> 111)

To convert the binary to octal number system, we have to remember the table given below, to solve the problems in a quick way.

You can easily understand by the help of below example.

Explanation of above problem

To convert a binary number (10011111) to its octal number, we have to follow these steps:

1. Group the binary digits of three from the right.

2. For the number 10011111, the grouping will be:

010 011 1111

2 3 7

Note: An extra '0' is put to the left of the binary number to make a complete group of 3 digits)

3. The octal equivalent of 10011111 is 237.

Second method to convert Binary Number to octal

• First convert the binary number to a decimal number

• convert the decimal number to octal

Let's understand by the help of below example

Explanation of above problem

To convert a binary number (10011111) to its octal number using another method, we have to follow these steps:

1. First we have to convert the binary number to a decimal number

2. For the number 10011111, the decimal equivalent will be: 53

3. Now we have to convert the decimal number to octal

4. The octal equivalent of 53 is 65.

By following those above two methods, you can easily convert any decimal to its hexadecimal equivalent.

Conclusion

In conclusion, converting binary to octal can be a straightforward process once you understand the basics. By grouping the binary digits into sets of three and assigning each set a corresponding octal digit, you can quickly convert between the two number systems.

Remember to start from the rightmost digit and work your way towards the left, ensuring that each binary digit is accounted for.

Another method is to convert binary number to its decimal number and then convert the decimal number to its octal equivalent.

With practice, converting binary to octal will become second nature, and you will be able to effortlessly convert between these number systems.