Use the below **binary converter** to convert Binary values to Decimal, Hexadecimal and Octal values.

Binary Number | _{2} | |

Decimal Number | _{10} | |

Octal Number | _{8} | |

Hexadecimal Number | _{16} |

Enter any binary number to this binary converter and click on convert button to convert binary to decimal, hexadecimal and octal.

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## 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.

## Decimal Number

Whole number, a decimal point and a fractional value combines to form a decimal number. The decimal point separates the whole number part from the fractional part of the number. Each digit of a decimal number can be any number from 0 to 9. Any value less than 1 is written to the right of decimal point. Decimal numbers are also known as *base-10 number* or counting numbers. Place value of decimal number varies as the whole number powers of 10 starting from the left of decimal point. Similarly, the place value of digits left to decimal point varies as the division of power of tens.

## Hexadecimal Number

Hexadecimal number system uses 16 different symbols to represent a numeric value. It uses numbers 0 to 9 and alphabets A to F for representation. . The place value of each digits of an hexadecimal number varies as the whole number powers of 16 starting from the right (Least Significant Digit). The first single digit number in hexadecimal system is 0 and the last is F. Similarly, the first two digit hexadecimal number is 10 and the last is FF and so on. It is used as an alternative for binary numbers by developers and programmers.

## 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.

## Binary to decimal Conversion

### Example: Convert 1111_{2} to decimal number

A binary number can be converted into decimal number using the following formula:

Decimal Number = (D_{n} X 2^{n}+ …………… + D_{2} X 2^{2}+ D_{1} X 2^{1}+ D_{0} X 2^{0}).

Where,

D_{n}– D_{0}→ digits of a binary number.

**Decimal number** = (1 X 2^{3} + 1 X 2^{2} + 1 X 2^{1 }+ 1 X 2^{0}) = 8 + 4 + 2 + 1 = 15_{10}

### Read More: How to convert a binary number to a decimal number

## Binary to Octal Conversion

### Example: Convert 1111_{2} to octal number

Split binary number into sets of three digits starting from the LSB. Note down the decimal number corresponding to each sets of three digits to convert binary number to octal number.

In this example 1111, 1111 can be rewritten as 001-111. Writing down the decimal number corresponding to the digits: 001→1 ,111→1.

So 1111_{2} = 17_{8}

## Binary to Hexadecimal Conversion

### Example: Convert 1111_{2} to hexadecimal number

Split binary number into sets of four digits starting from the LSB. Note down the hexadecimal number corresponding to each sets of four digits to convert binary number to hexadecimal number. (Refer the below table).

In this example 1111, 1111 can be rewritten as 0000-1111. Writing down the decimal number corresponding to the digits: 0000→0 ,1111→F.

So 1111_{2} = F_{16}

## Binary, Decimal, Octal and Hexadecimal conversion table

Binary | Decimal | Octal | Hexadecimal |
---|---|---|---|

0001 | 01 | 01 | 01 |

0010 | 02 | 02 | 02 |

0011 | 03 | 03 | 03 |

0100 | 04 | 04 | 04 |

0101 | 05 | 05 | 05 |

0110 | 06 | 06 | 06 |

0111 | 07 | 07 | 07 |

1000 | 08 | 10 | 08 |

1001 | 09 | 11 | 09 |

1010 | 10 | 12 | 0A |

1011 | 11 | 13 | 0B |

1100 | 12 | 14 | 0C |

1101 | 13 | 15 | 0D |

1110 | 14 | 16 | 0E |

1111 | 15 | 17 | 0F |

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