Binary to Octal Converter

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.

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

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.

3. You can add leading zeros to make the groups.

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​(11001)2​ to an octal number.

1. First, we will arrange the digits of the number into groups of three bits, i.e., 011  001011  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→3011→3
   001→1001→1

4. Hence the octal equivalent of the binary number (11001)2​(11001)2​ is (31)8​(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.

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​(715)8​ to binary representation:

1. Using table I, we get that the binary equivalent of 77 is 111111.

2. Similarly, the binary equivalent of other digits are:
   1→0011→001
   5→1015→101

3. Hence, the binary equivalent of (715)8​(715)8​ is (111001101)2​(111001101)2​.

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​(11001)2​ to an octal number:

1. Choose the binary to octal option.

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.