**INFORMATION**

**HEXADECIMAL AND DECIMAL NUMBERS**

Binary, octal, decimal and hexadecimal numbering systems are commonly used in mathematics, computer science and electrical engineering.

**Hexadecimal Numbering System (Base 16):** In the hexadecimal system, numbers are represented using sixteen digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. The values of the letters used in hexadecimal digits are shown below.

Hexadecimal | A | B | C | D | E | F |
---|---|---|---|---|---|---|

Decimal | 10 | 11 | 12 | 13 | 14 | 15 |

The ones digit has a place value of 16^{0} = 1, the next digit to the left has a place value of 16^{1} = 16, then 16^{2} = 256, and so on. As we move one place to the left, the place value increases by a factor of 16.

**Decimal Numbering System (Base 10):** In the decimal system, numbers are represented using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit has a place value of 10 raised to a power depending on its position in the number.

**HEXADECIMAL TO DECIMAL CONVERSION**

Each hexadecimal number has a unique representation in decimal numbering system. Hexadecimal to decimal (hex to dec) conversion is the process of computing the equivalent decimal representation of a base 16 number. To convert a hexadecimal number to decimal we multiply each digit by its place value and add the products.

Each place value in hexadecimal can be represented by an exponential number with a base of 16. Exponent of the place value increases by 1 if we move 1 digit left and the exponent of the ones digit is equal to zero.

**BINARY TO DECIMAL CONVERSION EXAMPLES**

**EXAMPLE:**

**EXAMPLE:**

**Find the decimal equivalent of the number 1A3 _{16} in hexadecimal system.**

To find the decimal equivalent of this number, we multiply each digit by its place value and then sum up the products.

1A3_{16} = 1 · 16^{2} + 10 · 16^{1} + 3 · 16^{0}

= 1 · 256 + 10 · 16 + 3 · 1

= 256 + 160 + 3

= 419_{10}

In the equations above, we replaced A with 10 because the value of the letter A is 10.

**EXAMPLE:**

**EXAMPLE:**

**Find the decimal equivalent of the hexadecimal number B0.4 _{16}.**

The place values of B0.4_{16} are shown below.

Multiply those values with the corresponding digits and add the products. (Remember that hexadecimal B is equal to 11.)

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**HEXADECIMAL TO DECIMAL CONVERSION TABLE**

The table below shows the decimal equivalents of the smallest non-negative hexadecimal numbers up to 100.

0 | 1 | 2 |

3 | 4 | 5 |

6 | 7 | 8 |

9 | A | B |

C | D | E |

F | 10 | 11 |

12 | 13 | 14 |

15 | 16 | 17 |

18 | 19 | 1A |

1B | 1C | 1D |

1E | 1F | 20 |

21 | 22 | 23 |

24 | 25 | 26 |

27 | 28 | 29 |

2A | 2B | 2C |

2D | 2E | 2F |

30 | 31 | 32 |

33 | 34 | 35 |

36 | 37 | 38 |

39 | 3A | 3B |

3C | 3D | 3E |

3F | 40 | 41 |

42 | 43 | 44 |

45 | 46 | 47 |

48 | 49 | 4A |

4B | 4C | 4D |

4E | 4F | 50 |

51 | 52 | 53 |

54 | 55 | 56 |

57 | 58 | 59 |

5A | 5B | 5C |

5D | 5E | 5F |

60 | 61 | 62 |

63 | 64 |

WHAT IS HEXADECIMAL TO DECIMAL CONVERTER?

Hexadecimal to decimal converter,

- Computes the decimal equivalent of the entered number,
- Describes the solution step by step and
- Illustrates the place values.

HOW TO USE HEXADECIMAL TO DECIMAL CONVERTER?

You can use hexadecimal to decimal converter in two ways.

**USER INPUTS**You can enter a hexadecimal number into the input box and then click the '

CONVERT ' button. The result and explanations will appear below the calculator.**RANDOM INPUTS**You can click on the

**DIE ICON**next to the input box to generate a random hexadecimal number, which will be automatically entered into the calculator. The result and explanations will then appear below the calculator. You can also create your own examples and practice using this feature.**CLEARING THE INPUT BOX**To find the decimal equivalent of another hexadecimal number, click on the

**CLEAR**button to clear the input box.**COPYING & DOWNLOADING THE SOLUTION**You can copy the generated solution by clicking on the 'Copy Text' link located below the solution panel.

You can also download the solution as an image file with a .jpg extension by clicking on the 'Download Solution' link located at the bottom of the solution panel. You can then share the downloaded image file.