The **Binary System** is a positional numbering system that represents the numbers in base 2, thus using two different symbols. This system uses the symbols 0 and 1. The binary system is the system most used by computers and other similar devices, this because the digital systems work internally with two states (true or false, on or off). According to some ancient manuscripts, the binary system was already used in China 3000 years before Christ. Although this system is widely used by all electronic devices, it has a major drawback regarding the decimal or hexadecimal system. The representation of numbers in the binary system takes up a lot of space. For example, the number 900,000 which in base 10 can be written with six digits, in base 2 twenty digits are required.

The **Decimal System** is a positional numbering system that represents the numbers in base 10, thus using ten different symbols. The decimal word originates in Latin, *decem* which means precisely ten. The specialists and historians are unanimous in considering that this way of counting in base 10, is due to the ten fingers that we have in the hands. This system uses the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. These figures are called Indo-Arabic because they originated in the works initiated by Hindus and Arabs. In the decimal system, each set of ten units forms a new order. For example, ten tens are equivalent to a hundred; ten hundreds equals a thousand, and so on.

binary to decimal | binary to decimal |
---|---|

000001 (bin) = (dec) | 100101 (bin) = (dec) |

000010 (bin) = (dec) | 100111 (bin) = (dec) |

000100 (bin) = (dec) | 101000 (bin) = (dec) |

000111 (bin) = (dec) | 101010 (bin) = (dec) |

001000 (bin) = (dec) | 110000 (bin) = (dec) |

001010 (bin) = (dec) | 110010 (bin) = (dec) |

010010 (bin) = (dec) | 110100 (bin) = (dec) |

010111 (bin) = (dec) | 111000 (bin) = (dec) |

011001 (bin) = (dec) | 111101 (bin) = (dec) |

011111 (bin) = (dec) | 111111 (bin) = (dec) |

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