# 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 2^{3} 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.

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:

1_{2} = 1_{8}

110_{2} = 4 + 2 + 0 = 6_{8}

001_{2} = 0 + 0 + 1 = 1_{8}

111_{2} = 4 + 2 + 1 = 7_{8}

011_{2} = 0 + 2 + 1 = 3_{8}

So, 1110001111011_{2} in binary is equal to 16173_{8} 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 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 |