Convert from base 16 to base 10

Hexadecimal and decimal systems

The hexadecimal system has 16 digits. The digits 1 through 9 are the same as in the decimal system, then the decimal numbers 10 through 15 are replaced by the letters A, B, C, D, E, and F of the English alphabet.

The decimal system (also known as the base 10 system) is a standard system for representing integers and non-integer numbers (decimal numbers). It is an extension for non-integer numbers of the Hindu-Arabic numeral system.

Convert from base 16 to base 10

How to convert base 16 to base 10

Hex is a base 16 number system and decimal is a base 10 number system. Sometimes, we need to know the decimal equivalent of a hexadecimal number.

Here are the steps to convert from base 16 to base 10:

  • Get the decimal equivalent of the hexadecimal digit from the table.
  • Multiply each digit by the power of 16 (the exponent corresponds to the digit's position, the rightmost digit corresponds to the 0 position). For example, in 7DE, the E position is 0, the D position is 1, and the 7 position is 2.
  • Calculate the sum of all multiplications.

Here is an example:

7DE is a hexadecimal number

  • 7DE = (7 * 162) + (13 * 161) + (14 * 160)
  • 7DE = (7 * 256) + (13 * 16) + (14 * 1)
  • 7DE = 1792 + 208 + 14

7DE = 2014 (in decimal)

Convert from base 16 to base 10

Example of converting from base 16 to base 10:

  • (1D9)16 = (473)10
  • (80E1)16 = (32993)10
  • (10CE)16 = (4302)10

Conversion table from base 16 to base 10

Hexadecimal system Base 10 system
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

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