Decimal system (base 10)
The decimal number system is the standard and most commonly used system in everyday life. This numbering system uses the number 10 as the base. The decimal system includes 10 characters, which are numbers from 0 to 9. Specifically, 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
One of the oldest known number systems, the decimal number system was used by many ancient civilizations. The difficulty in expressing very large numbers in the decimal system was overcome by the Hindu-Arabic number system. The Hindu-Arabic numbering system provides the positions for the digits in a number. Each position is equivalent to a power of 10, starting with the rightmost position before the decimal point which is 100.
Numerical example 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 digit 6 after the decimal point is in the 1/10 position (10-1) and 7 is at the 1/100 position (10-2).
Therefore, no 2345.67 can also be represented as follows: (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 system (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 strings. Long binary contains only two values 1 and 0.
Base 10 to base 16 conversion table
Base 10 number system | Base 16 number 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 |
See more: