Convert from 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.
Convert from base 10 to base 16
Decimal system (base 10)
The decimal number system is the standard and most commonly used system in everyday life. This number system uses the number 10 as its base. The decimal system consists of 10 symbols, which are the numbers 0 through 9. Specifically, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
As one of the oldest known number systems, the decimal system was 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 provides positions for the digits in a number. Each position corresponds to a power of 10, starting with the rightmost position before the decimal point, which is 100.
For example, the number 2345.67 in decimal:
- The digit 5 is in the units place (100 = 1),
- The digit 4 is in the tens place (101)
- The digit 3 is in the hundreds place (102)
- The digit 2 is in the thousands place (103)
- Meanwhile, the 6 after the decimal point is in the 1/10 position (10-1) and the 7 is in the 1/100 position (10-2).
Therefore, the number 2345.67 can also be represented as: (2 * 103) + (3 * 102) + (4 * 101) + (6 * 10-1) + (7 * 10-2).
Example of converting base 10 to base 16:
- (79)10 = (4F)16
- (120)10 = (78)16
- (1728)10 = (6C0)16
Hexadecimal (base 16)
The Hexadecimal, Hex or hexadecimal number system uses a base 16 number system and is a popular choice for representing long binary values, as their format is much more compact and easier to understand than long binary strings consisting of only 2 values 1 and 0.
Base 10 to Base 16 Conversion Table
| Base 10 system | Hexadecimal system |
|---|---|
| 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 |
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