HEX number:

DECIMAL number:

A regular decimal number is the sum of the digits multiplied with power of 10.

137 in base 10 is equal to each digit multiplied with its corresponding power of 10:

137_{10} = 1×10^{2}+3×10^{1}+7×10^{0}
= 100+30+7

Hex numbers are read the same way, but each digit counts power of 16 instead of power of 10.

For hex number with n digits:

*d _{n-1} ... d_{3} d_{2} d_{1} d_{0}*

Multiply each digit of the hex number with its corresponding power of 16 and sum:

decimal = *d _{n-1}×16^{n-1}+...+d_{3}×16^{3}+d_{2}×16^{2}+d_{1}×16^{1}+d_{0}×16^{0}*

3B in base 16 is equal to each digit multiplied with its
corresponding 16^{n}:

3B_{16} = 3×16^{1}+11×16^{0}
= 48+11 = 59_{10}

E7A9 in base 16 is equal to each digit multiplied with its
corresponding 16^{n}:

E7A9_{16} = 14×16^{3}+7×16^{2}+10×16^{1}+9×16^{0}
= 57344+1792+160+9 = 59305_{10}

0.8 in base 16:

0.8_{16} = 0×16^{0}+8×16^{-1}
= 0+0.5 = 0.5_{10}

Decimal | Hexadecimal |
---|---|

0 | 0 |

1 | 1 |

2 | 2 |

3 | 3 |

4 | 4 |

5 | 5 |

6 | 6 |

7 | 7 |

8 | 8 |

9 | 9 |

10 | A |

11 | B |

12 | C |

13 | D |

14 | E |

15 | F |

**Decimal** number system is the most commonly used and
the most familiar one to the general public. It is also known as *Base
10 numbering* system since it is based on 10 following symbols:
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. In decimal system, every digit has
its own position as well as the decimal point. I.e. the number 356.74
has 4 in the Hundredths position, 7 in the Tenths position, 6 in the
Units position, 5 in the Tens position, and 3 in the Hundreds
position. *Decimal number system* is also one of the oldest
known numeral system, which is historically related to Hindu-Arabic
numeral system.

**Hex**, or *hexadecimal*, is a number system of
base 16. This number system is especially interesting because in our
casually used decimal system we have only 10 digits to represent
numbers. As hex system has 16 digits, the extra needed 6 digits are
represented by the first 6 letters of English alphabet. Hence, **hex**
digits are 0,1,2,3,4,5,6,7,8 and 9 A, B, C, D, E, F. This number
system is the most commonly used in mathematics and information
technologies. I.e. in html programming colors can be represented by a
6-digit *hexadecimal number*: FFFFFF represents white, 000000
represents black, and so on.

- (79)
_{10}= (4F)_{16} - (120)
_{10}= (78)_{16} - (1728)
_{10}= (6C0)_{16}

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