Hexadecimal and decimal systems
The hexadecimal system has 16 digits. The digits 1 to 9 are the same as in the decimal system, followed by the decimal numbers 10 to 15 being replaced by the letters A, B, C, D, E and F of the English alphabet.
The decimal system (also known as base 10) is the standard system for representing integers and non-integers (decimal numbers). This is an extension to the non-integer numbers of the Hindu-Arabic number system.
How to convert base 16 to base 10
Hex (hexadecimal system) is the base 16 number system and the decimal system is the base 10 number system. Sometimes, we need to know the equivalent value in the decimal system 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 is equivalent to the digit's position, the rightmost digit is equivalent to the 0 position). Example in 7DE, location E is 0, position D is 1 and position 7 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)
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
Base 16 number system | Base 10 number 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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