# Binary to Octal Converter

Created by Purnima Singh, PhD
Reviewed by Steven Wooding
Last updated: Nov 03, 2022

The binary to octal converter allows you to switch between numbers in binary and octal representations.

If you don't know what binary and octal number systems are, worry not! Continue reading this article to understand the binary and octal number systems and the difference between them. You will also learn how to convert binary to octal and vice versa.

We also have a tool to that can help you perform binary arithmetic operations easily. Check out the binary calculator.

## Binary and octal number systems

Binary and octal are two different number systems that use different sets of symbols to represent numbers.

To understand this, let us take the example of our favorite, the decimal number system, which uses the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to represent any number.

In the same way, the binary number system uses only two symbols, 0 and 1 (hence the name base 2), to represent any number. Whereas, the octal number system (or the base eight system) uses eight symbols: 0, 1, 2, 3, 4, 5, 6, and 7.

As shown in Table I, we can represent each octal digit using three binary numbers.

Table I: Octal and its corresponding binary equivalent system.

Octal digit

Binary equivalent

0

000

1

001

2

010

3

011

4

100

5

101

6

110

7

111

In the following sections, we will see the steps involved in the conversion of binary to octal number systems.

## How to convert binary to octal

To convert a binary number to an octal number, we will use a very straightforward approach:

1. Starting at the last digit, i.e., the rightmost digit, arrange the digits into groups of three bits.

2. Now, convert each group into the corresponding octal digit using Table I.

You must have already realized that the steps involved in binary to octal conversion are relatively simple. Let us understand this using an example. We will convert the binary number $(11001)_2$ to an octal number.

1. First, we will arrange the digits of the number into groups of three bits, i.e., $011\ \ 001$.

2. Note that we have added a leading zero to make the group.

3. Using Table I, now we will convert each group into the corresponding octal digit:

$011 \rightarrow 3$
$001 \rightarrow 1$

4. Hence the octal equivalent of the binary number $(11001)_2$ is $(31)_8$.

If you want to learn how to convert binary numbers to hexadecimal or decimal numbers, we recommend checking out our binary to hexadecimal and binary to decimal converters.

## How to convert octal to binary

The conversion of an octal number into a binary number is also straightforward. Just replace every digit with its equivalent 3-bit binary number (as shown in Table I).

For example, let us convert $(715)_8$ to binary representation:

1. Using table I, we get that the binary equivalent of $7$ is $111$.

2. Similarly, the binary equivalent of other digits are:
$1 \rightarrow 001$
$5 \rightarrow 101$

3. Hence, the binary equivalent of $(715)_8$ is $(111001101)_2$.

## Using the binary to octal converter – An example

Now let us see how we can use the binary to octal converter to solve the same problems. First, we will convert the binary number $(11001)_2$ to an octal number:

1. Using the drop-down menu, choose binary to octal.

2. Enter the number 11001 in the field binary input.

3. The converter will display its octal equivalent, i.e., 31.

4. For converting a number from the octal to binary representation, choose the appropriate option and enter the number 715 in the field octal input.

5. The octal to binary converter will display the number 111001101.

## FAQ

### What is the octal equivalent of the binary number 110110001010?

To find the octal equivalent of the binary number 110110001010, follow the given steps:

1. Organise the digits of the number in groups of three, i.e., 110 110 001 010.

2. Find out the octal equivalent of the four groups:
110 - 6
110 - 6
001 - 1
010 - 2

3. The octal equivalent of the binary number 110110001010 is 6612.

### What is the octal equivalent of 1011 1101?

275. Starting from the rightmost digit and grouping the digits of the given number in sets of three, we get 010 111 101. The octal equivalent of these groups is 275.

### What is the binary equivalent of octal number 472?

100111010. The binary equivalent of 4 is 100, 7 is 111, and that of 2 is 010. Arranging these digits, we will get 100111010 which is the binary equivalent of octal number 472.

### What is the base of binary number system?

The base of the binary number system is 2. It means that the binary number system has only two possible digits or symbols, namely, 0 and 1. All the numbers in the binary system can be expressed using these two digits.

Purnima Singh, PhD
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