# binary

Binary describes a numbering scheme in which there are only two possible values for each digit: 0 and 1. The term also refers to any digital encoding/decoding system in which there are exactly two possible states. In digital data memory, storage, processing, and communications, the 0 and 1 values are sometimes called "low" and "high," respectively.

A bit (short for binary digit) is the smallest unit of data on a computer; each bit has a single value of either 1 or 0. Executable (ready-to-run) programs are often identified as binary files and given a file name extension of ".bin.” Programmers often call executable files *binaries*.

Binary numbers look strange when they are written out directly. This is because the digits' weight increases by powers of 2, rather than by powers of 10. In a digital numeral, the digit furthest to the right is the "ones" digit; the next digit to the left is the "twos" digit; next comes the "fours" digit, then the "eights" digit, then the "16s" digit, then the "32s" digit, and so on. The decimal equivalent of a binary number can be found by summing all the digits. For example, the binary 10101 is equivalent to the decimal 1 + 4 + 16 = 21:

DECIMAL = 21 |
64 | 32 | 16 |
8 | 4 |
2 | 1 |

BINARY = 10101 |
0 | 0 | 1 |
0 | 1 |
0 | 1 |

The numbers from decimal 0 through 15 in decimal, binary, octal, and hexadecimal form are listed below.

DECIMAL |
BINARY |
OCTAL |
HEXA-DECIMAL |

0 | 0 | 0 | 0 |

1 | 1 | 1 | 1 |

2 | 10 | 2 | 2 |

3 | 11 | 3 | 3 |

4 | 100 | 4 | 4 |

5 | 101 | 5 | 5 |

6 | 110 | 6 | 6 |

7 | 111 | 7 | 7 |

8 | 1000 | 10 | 8 |

9 | 1001 | 11 | 9 |

10 | 1010 | 12 | A |

11 | 1011 | 13 | B |

12 | 1100 | 14 | C |

13 | 1101 | 15 | D |

14 | 1110 | 16 | E |

15 | 1111 | 17 | F |

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