## Binary number

Binary numbering system uses only two symbols 0 and 1. Each digits of a binary number is referred to as bits. Binary system is also known as base -2 system. Each digit is represented by the increasing power of 2 from the LSB (Least Significant Bit). Binary system is the heart of digital electronics and is used for information flow. In digital electronics, 0 and 1 are used to denote logic states, high and low. Arithmetic operations are also possible in binary system.

## Octal Number

Octal numbers use digits from 0-7 only. It is known as base-8 number. The place value of each digits of an octal number varies as the whole number powers of 8 starting from the right (Least Significant Digit). The first single digit number in octal system is 0 and the last is 7. Similarly, the first two digit octal number is 10 and the last is 77 and so on. Octal number system was widely used in early computers.

## How to convert a binary number to octal:

### Step 1:

To convert any binary number to octal, check whether the number of digits of the binary number is a multiple of 3.

### Step 2:

If the number of digits of the binary number is a multiple of 3 proceed to step 3. Otherwise add zeros to the left of the digits.

### Step 3:

Divide the digits of binary number into groups of 3 digits.

### Step 4:

Refer the below table and note down octal value correspond to each group of digits.

Binary Number | Octal Number |
---|---|

000 | 0 |

001 | 1 |

010 | 2 |

011 | 3 |

100 | 4 |

101 | 5 |

110 | 6 |

111 | 7 |

### Step 5:

Join the results together to get the converted octal number.

## Use Binary to Octal convertor

## Example 1:

### Convert 11010_{2} to Octal.

### Step 1:

To convert any binary number to hexadecimal, check whether the number of digits of the binary number is a multiple of 3.

11010_{2}, there are 5 digits, that is not a multiple of 3.

### Step 2:

If the number of digits of the binary number is a multiple of 3 proceed to step 3. Otherwise add zeros to the left of the digits.

11010_{2} can be rewritten as 011010_{2}

### Step 3:

Divide the digits of binary number into groups of 3 digits.

011 010

### Step 4:

Refer the table and note down the octal value correspond to each group of digits.

011 | 010 |

3 | 2 |

### Step 5:

Join the results together to get the converted octal number.

11010_{2} = 32_{8}

## Example 2:

### Convert 110101_{2} to Octal.

### Step 1:

To convert any binary number to octal, check whether the number of digits of the binary number is a multiple of 3.

110101_{2}, there are 6 digits, that is a multiple of 3. So, we can move to step 3.

### Step 3:

Divide the digits of binary number into groups of 3 digits.

110 101

### Step 4:

Refer the table and note down the octal value correspond to each group of digits.

110 | 101 |

6 | 5 |

Step 5:

Join the results together to get the converted octal number.

110101_{2} = 65_{8}