# Decimal to Hexadecimal Converter

To use this **decimal to hex converter** tool, you have to type a decimal value like 79 into the left field below,
and then hit the Convert button. Therefore, you can convert up to 19 decimal characters (max. value of 9223372036854775807) to hex.

### Decimal to hex conversion result in base numbers

## Decimal System

**The decimal numeral system** is the most commonly used and the standard system in daily life. It uses the number 10 as its base (radix). Therefore, it has 10 symbols: The numbers from 0 to 9; namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

As one of the oldest known numeral systems, the **decimal numeral system** has been used by many ancient civilizations. The difficulty of representing very large numbers in the decimal system was overcome by the Hindu–Arabic numeral system. The Hindu-Arabic numeral system gives positions to the digits in a number and this method works by using powers of the base 10; digits are raised to the n^{th} power, in accordance with their position.

For instance, take the number 2345.67 in the decimal system:

- The digit 5 is in the position of ones (10
^{0}, which equals 1), - 4 is in the position of tens (10
^{1}) - 3 is in the position of hundreds (10
^{2}) - 2 is in the position of thousands (10
^{3}) - Meanwhile, the digit 6 after the decimal point is in the tenths (1/10, which is 10
^{-1}) and 7 is in the hundredths (1/100, which is 10^{-2}) position - Thus, the number 2345.67 can also be represented as follows:
(2 * 10
^{3}) + (3 * 10^{2}) + (4 * 10^{1}) + (5 * 10^{0}) + (6 * 10^{-1}) + (7 * 10^{-2})

## Hexadecimal System (Hex System)

The **hexadecimal system (shortly hex)**, uses the number 16 as its base (radix). As a base-16 numeral system, it uses 16 symbols. These are the 10 decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and the first six letters of the English alphabet (A, B, C, D, E, F). The letters are used because of the need to represent the values 10, 11, 12, 13, 14 and 15 each in one single symbol.

Hex is used in mathematics and information technologies as a more friendly way to represent binary numbers. Each hex digit represents four binary digits; therefore, hex is a language to write binary in an abbreviated form.

Four binary digits (also called nibbles) make up half a byte. This means one byte can carry binary values from 0000 0000 to 1111 1111. In hex, these can be represented in a friendlier fashion, ranging from 00 to FF.

In html programming, colors can be represented by a 6-digit hexadecimal number: FFFFFF represents white whereas 000000 represents black.

### How to Convert Decimal to Hex

**Decimal to hexadecimal conversion** can be achieved by applying the repeated division and remainder algorithm. Simply put, the decimal number is repeatedly divided by the radix 16. In between these divisions, the remainders give the hex equivalent in reverse order.

Here is how to convert decimal to hex step by step:

**Step 1**: If the given decimal number is less than 16, the hex equivalent is the same. Remembering that the letters A, B, C, D, E and F are used for the values 10, 11, 12, 13, 14 and 15, convert accordingly. For example, the decimal number 15 will be F in hex.**Step 2**: If the given decimal number is 16 or greater, divide the number by 16.**Step 3**: Write down the remainder.**Step 4**: Divide the part before the decimal point of your quotient by 16 again. Write down the remainder.**Step 5**: Continue this process of dividing by 16 and noting the remainders until the last decimal digit you are left with is less than 16.**Step 6**: When the last decimal digit is less than 16, the quotient will be less than 0 and the remainder will be the digit itself.**Step 7**: The last remainder you get will be the most significant digit of your hex value while the first remainder from Step 3 is the least significant digit. Therefore, when you write the remainders in reverse order - starting at the bottom with the most significant digit and going to the top- you will reach the hex value of the given decimal number.

Now, let’s apply these steps to, for example, the decimal number (501)_{10}

Step 1: As 501 is greater than 16, divide by 16. 501 ÷ 16 = 31.3125 Step 2: To calculate the remainder, you need to multiply the part after the decimal point by 16. 0.3125 * 16 = 5 So the first remainder (and the least significant digit in hex) is 5. Step 3: Divide 31 (the part of the quotient that is before the decimal point) by 16. 31 ÷ 16 = 1.9375 Step 4: Calculate the remainder. 0.9375 * 16 = 15 Step 5: Divide the integer part of the last quotient by 16. 1 ÷ 16 = 0.0625 Step 6: Calculate the remainder. 0.0625 * 16 = 1 Step 7: The remainders written from below to top give you the hex values 1, 15 and 5. Since 15 equals F in the hexadecimal numerals, (501)_{10}= (1F5)_{16}

#### Decimal to Hex Conversion Examples

Example 1: (4253)_{10} = (109D)_{16}

4253 ÷ 16 = 265.8125 0.8125 * 16 = 13 (Remainder 13, equivalent to D in hexadecimal) 265 ÷ 16 = 16.5625 0.5625 * 16 = 9 (Remainder 9) 16 ÷ 16 = 1 (Remainder 0) 1 ÷ 16 = 0.0625 0.00625 * 16: 1 (Remainder 1) Read the remainders from the most significant to the least - from bottom to top: 109D. 109D the hex equivalent of (4253)_{10}

Example 2: (16)_{10} = (10)_{16}

16 ÷ 16 = 1 (Remainder 0) 1 ÷ 16 = 0.0625 0.00625 * 16: 1 (Remainder 1)

Example 3: (45)_{10} = (2D)_{16}

45 ÷ 16 = 2.8125 0.8125 * 16 = 13 (Remainder 13, equivalent to D in hexadecimal) 2 ÷ 16 = 0.125 0.125 * 16 = 2 (Remainder 2)

#### Decimal Hex Conversion Chart

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 |