# Binary to Decimal, Hexadecimal and ASCII Converter

## Convert between binary, decimal and hexadecimal numbers

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### Binary - to Decimal, Hexadecimal and ASCII Converter

Click on the binary number buttons to toggle between 0 and 1 for each bit:

unsigned binary number (8 bits, one byte) | ||||||||
---|---|---|---|---|---|---|---|---|

2^{7} | 2^{6} | 2^{5} | 2^{4} | 2^{3} | 2^{2} | 2^{1} | 2^{0} | |

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | |

decimal number | 0 | |||||||

hexadecimal number | 0 | |||||||

ASCII |

A binary number is a number expressed in the binary numeral system or **base 2** numeral system. A binary number can express any number by using only two digits: 0 and 1. The calculator above converts binary numbers with *1 to 8 bits* (*one byte*) to the decimal or hexadecimal equivalents.

The default 8 bit (one byte) binary number *10100100* is calculated to the decimal equivalent:

*10100100*

*= 1 2^{7} + 0 2^{6} + 1 2^{5} + 0 2^{4} + 0 2^{3} + 1 2^{2} + 0 2^{1} + 0 2^{0} *

*= 128 + 0 + 32 + 0 + 0 + 4 + 0 + 0*

*= 164 *

8 bits or byte can be used to represent an ASCII (American Standard Code for Information Interchange) alphabetic character - like the binary number* 01000001*, or decimal number *65*, representing *A.*

### Decimal - to Binary, Hexadecimal and ASCII Converter

decimal number | |
---|---|

binary number | |

hexadecimal number | |

ASCII |

The standard numeral system is called decimal with **base 10** and uses 10 symbols: 0,1,2,3,4,5,6,7,8,9.

### Hexadecimal - to Binary, Decimal and ASCII Converter

hexadecimal number | |
---|---|

binary number | |

decimal number | |

ASCII |

The hexadecimal (also base 16, or hex) is a positional numeral system with **base 16**.

The hexadecimal system use sixteen distinct symbols with *0–9 *representing the values zero to nine and *A, B, C, D, E, F (or a, b, c, d, e, f)* representing the values ten to fifteen.

The default hexadecimal number *a4* from the calculator above can be converted to its decimal equivalent:

*a4*

*= a _{16} 16^{1} + 4_{16} 16^{0 }*

*= 10 16 ^{1} + 4 16^{0 }*

*= 160 + 4*

*= 164*

The hexadecimal number *a4* from the calculator above can be converted to its decimal equivalent:

*a4b3*

*= a _{16} 16^{3} + 4_{16} 16^{2 }+* b

_{16}16

^{1}+ 3

_{16}16

^{0 }

*= 10 16 ^{3} + 4 16^{2}* + 11 16

^{1}+ 3 16

^{0 }

*=40960 + 1024 + 176 + 3*

*= 42163*

#### Hexadecimal vs. Decimal and Binary Numbers

Hexadecimal Number | |||||||||||||||

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | a | b | c | d | e | f |

Decimal Number | |||||||||||||||

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |

Binary Number | |||||||||||||||

0000 | 0001 | 0010 | 0011 | 0100 | 0101 | 0110 | 0111 | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 |

Each hexadecimal digit represents four binary bits - a nibble. Four digital bits can represent up to 16 different values. Two nibbles with 8 bits is a byte. Computers use mostly bytes or multiplies of bytes (16, 32, 64 .. bits) in their operations.

Binary representation of the hexadecimal number

*a4*

*= 1010 0100*

Binary representation of the hexadecimal number

*a4b3*

*= 1010 0100 1011 0011 *

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