- Numeral system
- Binary numeral system
- Octal numeral system
- Decimal numeral system
- Hex Numeral system
- Numeral system conversion table

## Numeral system

*b* - numeral system base

*d _{n} - *the n-th digit

*n* - can start from negative number if the number has a fraction part.

*N*+1 - the number of digits

## Binary Numeral System - Base-2

Binary numbers uses only 0 and 1 digits.

B denotes binary prefix.

#### Examples:

10101_{2} = 10101B = 1×2^{4}+0×2^{3}+1×2^{2}+0×2^{1}+1×2^{0
}= 16+4+1= 21

10111_{2} = 10111B = 1×2^{4}+0×2^{3}+1×2^{2}+1×2^{1}+1×2^{0
}= 16+4+2+1= 23

100011_{2} = 100011B = 1×2^{5}+0×2^{4}+0×2^{3}+0×2^{2}+1×2^{1}+1×2^{0
}=32+2+1= 35

## Octal Numeral System - Base-8

Octal numbers uses digits from 0..7.

#### Examples:

27_{8} = 2×8^{1}+7×8^{0 }= 16+7 = 23

30_{8} = 3×8^{1}+0×8^{0 }= 24

4307_{8} = 4×8^{3}+3×8^{2}+0×8^{1}+7×8^{0}= 2247

## Decimal Numeral System - Base-10

Decimal numbers uses digits from 0..9.

These are the regular numbers that we use.

#### Example:

2538_{10} = 2×10^{3}+5×10^{2}+3×10^{1}+8×10^{0}

## Hexadecimal Numeral System - Base-16

Hex numbers uses digits from 0..9 and A..F.

H denotes hex prefix.

#### Examples:

28_{16} = 28H = 2×16^{1}+8×16^{0 }= 40

2F_{16} = 2FH = 2×16^{1}+15×16^{0 }= 47

BC12_{16} = BC12H = 11×16^{3}+12×16^{2}+1×16^{1}+2×16^{0}= 48146

## Numeral systems conversion table

Decimal
Base-10 |
Binary Base-2 |
Octal Base-8 |
Hexadecimal Base-16 |
---|---|---|---|

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 |

16 | 10000 | 20 | 10 |

17 | 10001 | 21 | 11 |

18 | 10010 | 22 | 12 |

19 | 10011 | 23 | 13 |

20 | 10100 | 24 | 14 |

21 | 10101 | 25 | 15 |

22 | 10110 | 26 | 16 |

23 | 10111 | 27 | 17 |

24 | 11000 | 30 | 18 |

25 | 11001 | 31 | 19 |

26 | 11010 | 32 | 1A |

27 | 11011 | 33 | 1B |

28 | 11100 | 34 | 1C |

29 | 11101 | 35 | 1D |

30 | 11110 | 36 | 1E |

31 | 11111 | 37 | 1F |

32 | 100000 | 40 | 20 |

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