# HEX to Decimal

## Hexadecimal to Decimal Converter

Enter a hex value, such as 1E, in the left field below and click the Convert button to utilize this online hex to decimal converter tool. You can convert up to 16 hex characters to decimal, with a maximum value of 7fffffffffffff.

## Hexadecimal System (Hex System)

The basis of the hexadecimal system (abbreviated hex) is 16. (radix). It employs 16 symbols since it is a base-16 numeric system. The first six letters of the English alphabet are A, B, C, D, E, and F, and the first ten decimal numbers are 0 through 9 (0, 1, 2, 3, 5, 6, 7, and 8). The need to represent the numbers 10, 11, 12, 13, 14, and 15 in a single symbol necessitates the employment of the letters.

In mathematics and information technology, hex is employed to represent binary integers because it is more aesthetically pleasing. Hex is a binarily abridged language since each hex digit represents four binary digits.

A half-byte (also known as a nibble) consists of four binary digits. These can be more amiably represented in hex, where they range from 00 to FF. Accordingly, a single byte can store binary values between 0000 0000 and 1111 1111.

In HTML programming, colors are denoted by a 6-digit hexadecimal number. For example, white is denoted by FFFFFF, whereas black is denoted by 000000.

## Decimal System

The decimal numeral system is the most widely used and accepted system in daily life. It bases itself on the number 10. (radix). Consequently, it has ten symbols: The digits 0 through 9, namely 0, 1, 2, 3, 4, 5, 6, 7, and 9.

Many ancient civilizations used the decimal numeral system, which is one of the earliest numeral systems that is now known. The Hindu-Arabic numeral system solved the problem of representing huge numbers in the decimal system. The Hindu-Arabic numeral system assigns positions to the digits of a number. This system uses powers of base 10 to calculate numbers, and the digits are raised to the nth power according to their placements.

**Consider the decimal number 2345.67 as an example:**

- The number 5 is in the place of ones (100 equals 1), and the number 4 is in the place of tens (101)
- 3 is in the hundreds position (102)
- 2 is in the thousands position (103)

In the meantime, the digits 6 and 7 are in the tenths (1/10, which is 10-1) and the hundredths (1/100, which is 10-2) positions, respectively, after the decimal point.

Therefore, the following is another way to express the number 2345.67: (2 * 103) + (3 * 102) + (4 * 101) + (5 * 100) + (6 * 10-1) + (7 * 10-2)

## How to convert from hex to decimal?

- The sum of the digits multiplied by 10 is a standard decimal number.
- Each digit multiplied by the matching power of 10 results in 137 in base 10:
- 13710 = 1×102+3×101+7×100 = 100+30+7
- The same rules apply to reading hex numbers. However, each digit counts as a power of 16 rather than 10.

**For hex numbers with n digits:**

... dn-1... d3 d2 d1 d0

Multiply each hex digit by the matching power of 16 and add the results:

Decimal: dn-116n-1 +... + d3163, d2162, d1161, and d0160

#### Example:

0.8 in base 16:

0.8_{16} = 0×16^{0}+8×16^{-1} = 0+0.5 = 0.5_{10}

## Hex to decimal conversion table

Hex base 16 |
Decimal base 10 |
Calculation |
---|---|---|

0 | 0 | - |

1 | 1 | - |

2 | 2 | - |

3 | 3 | - |

4 | 4 | - |

5 | 5 | - |

6 | 6 | - |

7 | 7 | - |

8 | 8 | - |

9 | 9 | - |

A | 10 | - |

B | 11 | - |

C | 12 | - |

D | 13 | - |

E | 14 | - |

F | 15 | - |

10 | 16 | 1×16^{1}+0×16^{0} = 16 |

11 | 17 | 1×16^{1}+1×16^{0} = 17 |

12 | 18 | 1×16^{1}+2×16^{0} = 18 |

13 | 19 | 1×16^{1}+3×16^{0} = 19 |

14 | 20 | 1×16^{1}+4×16^{0} = 20 |

15 | 21 | 1×16^{1}+5×16^{0} = 21 |

16 | 22 | 1×16^{1}+6×16^{0} = 22 |

17 | 23 | 1×16^{1}+7×16^{0} = 23 |

18 | 24 | 1×16^{1}+8×16^{0} = 24 |

19 | 25 | 1×16^{1}+9×16^{0} = 25 |

1A | 26 | 1×16^{1}+10×16^{0} = 26 |

1B | 27 | 1×16^{1}+11×16^{0} = 27 |

1C | 28 | 1×16^{1}+12×16^{0} = 28 |

1D | 29 | 1×16^{1}+13×16^{0} = 29 |

1E | 30 | 1×16^{1}+14×16^{0} = 30 |

1F | 31 | 1×16^{1}+15×16^{0} = 31 |

20 | 32 | 2×16^{1}+0×16^{0} = 32 |

30 | 48 | 3×16^{1}+0×16^{0} = 48 |

40 | 64 | 4×16^{1}+0×16^{0} = 64 |

50 | 80 | 5×16^{1}+0×16^{0} = 80 |

60 | 96 | 6×16^{1}+0×16^{0} = 96 |

70 | 112 | 7×16^{1}+0×16^{0} = 112 |

80 | 128 | 8×16^{1}+0×16^{0} = 128 |

90 | 144 | 9×16^{1}+0×16^{0} = 144 |

A0 | 160 | 10×16^{1}+0×16^{0} = 160 |

B0 | 176 | 11×16^{1}+0×16^{0} = 176 |

C0 | 192 | 12×16^{1}+0×16^{0} = 192 |

D0 | 208 | 13×16^{1}+0×16^{0} = 208 |

E0 | 224 | 14×16^{1}+0×16^{0} = 224 |

F0 | 240 | 15×16^{1}+0×16^{0} = 240 |

100 | 256 | 1×16^{2}+0×16^{1}+0×16^{0} = 256 |

200 | 512 | 2×16^{2}+0×16^{1}+0×16^{0} = 512 |

300 | 768 | 3×16^{2}+0×16^{1}+0×16^{0} = 768 |

400 | 1024 | 4×16^{2}+0×16^{1}+0×16^{0} = 1024 |