# Binary to Octal Converter

Enter a binary number below to convert it to octal.

## How to Convert Binary to Octal

The binary number system is a base 2 number system since it only uses the digits 0 and 1. Octal is a base 8 number system since it uses eight digits: 0, 1, 2, 3, 4, 5, 6 & 7.

Binary and octal numbers are often used in computing applications, so it’s fairly common to need to convert from one to the other.

The base 8 system is often used in legacy computing applications because a single octal digit can represent three binary bits, which are cleanly divisible in 6, 12, 24, and 36-bit computer systems.

Most modern computer systems, however, are 16, 32, or 64-bit systems. Since these are cleanly divisible into base 16 numbers, the hexadecimal system is much more common.

You can convert from binary to octal in a few simple steps.

### Step One: Split into Groups of Three Digits

The first step is to break the binary number into groups of three digits, starting from the right to the left. The reason for this is that a group of three base 2 numbers, or 23 is equal to 8, which is evenly divisible into the base 8 number system.

For example, the binary number 1110001111011 can be broken into the following groups:

1110001111011
(1)(110)(001)(111)(011)

It’s ok if the first group does not have three digits. You can also add additional zeros to precede the digits in the first group so that there are three digits.

### Step Two: Convert Each Binary Group to an Octal Digit

At this point, each group of three binary digits can be converted to an octal digit using the following table.

#### 3-bit Binary Words to Octal Values

The following table shows the octal digits for each possible 3-bit word of binary digits.

3-bit binary words converted to the equivalent octal digits
Binary Word Octal Digit
000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7

Applying this to the binary number above that we split into groups of three digits:

12 = 18
1102 = 4 + 2 + 0 = 68
0012 = 0 + 0 + 1 = 18
1112 = 4 + 2 + 1 = 78
0112 = 0 + 2 + 1 = 38

So, 11100011110112 in binary is equal to 161738 in octal.

You can also use a tool like our binary converter to convert to decimal or hex.

### Binary to Octal Conversion Table

The table below shows binary numbers and the equivalent octal number values.

Binary numbers converted to the equivalent octal values
Binary Number Octal Number Decimal Number
0 0 0
1 1 1
10 2 2
11 3 3
100 4 4
101 5 5
110 6 6
111 7 7
1000 10 8
1001 11 9
1010 12 10
1011 13 11
1100 14 12
1101 15 13
1110 16 14
1111 17 15
10000 20 16
10001 21 17
10010 22 18
10011 23 19
10100 24 20
10101 25 21
10110 26 22
10111 27 23
11000 30 24
11001 31 25
11010 32 26
11011 33 27
11100 34 28
11101 35 29
11110 36 30
11111 37 31
100000 40 32
1000000 100 64
10000000 200 128
100000000 400 256
1000000000 1000 512
10000000000 2000 1024
100000000000 4000 2048