# Hexadecimal Number Systems

Contents

## Hexadecimal Number System

Following are the characteristics of a hexadecimal number system.

- Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.
- Letters represents numbers starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15.
- Also called base 16 number system
- Each position in a hexadecimal number represents a 0 power of the base (16). Example 16
^{0} - Last position in a hexadecimal number represents a x power of the base (16). Example 16
^{x}where x represents the last position – 1.

### Example

Hexadecimal Number: 19FDE_{16}

Calculating Decimal Equivalent:

Step | Binary Number | Decimal Number |
---|---|---|

Step 1 | 19FDE_{16} |
((1 x 16^{4}) + (9 x 16^{3}) + (F x 16^{2}) + (D x 16^{1}) + (E x 16^{0}))_{10} |

Step 2 | 19FDE_{16} |
((1 x 16^{4}) + (9 x 16^{3}) + (15 x 16^{2}) + (13 x 16^{1}) + (14 x 16^{0}))_{10} |

Step 3 | 19FDE_{16} |
(65536+ 36864 + 3840 + 208 + 14)_{10} |

Step 4 | 19FDE_{16} |
106462_{10} |

**Note: **19FDE_{16} is normally written as 19FDE.

## Hexadecimal Addition

Following hexadecimal addition table will help you greatly to handle Hexadecimal addition.

To use this table, simply follow the directions used in this example: Add: A_{16} and 5_{16}.Locate A in the X column then locate the 5 in the Y column. The point in sum area where these two columns intersect is the sum of two numbers.

A_{16} + 5_{16} = F_{16}.

### Example – Addition

## Hexadecimal Subtraction

The subtraction of hexadecimal numbers follows the same rules as the subtraction of numbers in any other number system. The only variation is in borrowed number. In the decimal system, you borrow a group of 10_{10}. In the binary system, you borrow a group of 2_{10}. In the hexadecimal system you borrow a group of 16_{10}.