#### RESULTS

1 | Hex Addition |

2 | Hex Subtraction |

3 | Hex Multiplication |

4 | Hex Division |

Our hexadecimal calculator allows you to perform the most famous 4 basic mathematical operations that are usually performed on decimal numbers. Here, you can perform addition, subtraction, multiplication and division on hex numerals as well.

It’s easier to do these operations on decimals but when it comes to hex symbols, the operations get trickier which an everyday person is not trained for.

Overview

The hex number system works virtually identically to the decimal and binary systems. Rather than making use of a base of 10 or 2 respectively, it has a base of 16 because it employs 16 digits with numbers from 0-9, just as the decimal system does, but also uses the letters A, B, C, D, E, and F (equivalent to a, b, c, d, e, f) to represent the numbers 10-15.

Every hex digit signifies 4 binary digits, called nibbles, which makes representing large binary numbers simpler. For instance, the binary value of \(011011100110011000011\) can be characterized as \(DCCC3\) in hex. This allows computing machines to compress huge binary values in a way that can be transformed between the two systems with ease.

Given below, are some general conversions between hexadecimal, binary, and decimal values:

Hex | Binary | Decimal |
---|---|---|

0 | 0 | 0 |

1 | 1 | 1 |

2 | 10 | 2 |

3 | 11 | 3 |

4 | 100 | 4 |

5 | 101 | 5 |

6 | 110 | 6 |

1 | 111 | 7 |

8 | 1000 | 8 |

9 | 1001 | 9 |

A | 1010 | 10 |

B | 1011 | 11 |

C | 1100 | 12 |

D | 1101 | 13 |

E | 1110 | 14 |

F | 1111 | 15 |

14 | 10100 | 20 |

3F | 111111 | 63 |

## Hex Addition

Hex addition employs the same rules as decimal addition with the only distinction being the added symbols i.e. A, B, C, D, E, and F. It can be quite convenient to have the decimal equivalent values of A to F. Down below, is a sample of hex addition.

### Example:

^{1}8 | ^{1}A | B | ||

+ | B | 7 | 8 | |

= | 1 | 4 | 2 | 3 |

In the example instance, B + 8 in decimal would be 11 + 8 = 19. 19 would be 13, since there is 1 set of 16, with 3 available. If you find it time-consuming, just use our calculator for hexadecimal addition.

## Hex Subtraction

The most important distinction between hexadecimal and decimal subtraction has to do with borrowing. When you borrow in hex, the "1" that is borrowed represents a base of 16 rather than that of 10.

The reason has to do with the column that is being borrowed from which is 16 times larger than the borrowing column in decimal subtraction.

### Example:

5 | D | ^{1}C | |

- | 3 | A | F |

= | 2 | 2 | 2 |

Hex Multiplication

Hexadecimal multiplication can be a bit confusing as the conversions between hexadecimal and decimal demand more effort as the numerals happen to be larger.

Shown below is an example of hex multiplication. To the right of the example, each of the multiplication and steps for addition are given. Bear in mind that all of the numerals employed are hexadecimal.

### Example:

F | A | 3 × A = 1E; 1 carried down to F | |||

x | C | 3 | 3 × F = 2D, + 1 = 2E | ||

2 | E | F | C × A = 78; 7 carried down to F | ||

+ | B | B | 8 | 0 | C × F = B4, + 7 = BB |

= | B | E | 6 | E |

Hex Division

Long division in hexadecimal is corresponding to long division in decimal, apart from the multiplication and subtraction that occur in hex.

For demonstrative purposes, the division example would be calculated in hexadecimal.

### Example:

`\( \space\stackrel{DEF}{\stackrel{12\sqrt{FACE}}{\stackrel{\underline{EA}}{\stackrel{10C}{\space\stackrel{\underline{FC}}{\space\stackrel{10E}{\stackrel{\underline{10E}}{\stackrel{0}{}}}}}}}} \)`

You can also check out our hex to binary and hex to decimal tools if you also want to convert data from one format to the other.