Decimal is a numeral system that uses ten digits from 0 to 9 to represent any number. It is also known as the base-10 system, as each digit's value is multiplied by a power of 10, depending on its position in the number.
The decimal system is widely used in everyday life, commerce, and science because it is intuitive and easy to understand. It allows for precise representation of quantities, fractions, and percentages, making it an essential tool for mathematics and accounting.
To convert a decimal number to another numeral system, such as binary or hexadecimal, you need to divide the number successively by the base of the target system and keep track of the remainders. For example, to convert the decimal number 255 to binary:
255 / 2 = 127 remainder 1
127 / 2 = 63 remainder 1
63 / 2 = 31 remainder 1
31 / 2 = 15 remainder 1
15 / 2 = 7 remainder 1
7 / 2 = 3 remainder 1
3 / 2 = 1 remainder 1
1 / 2 = 0 remainder 1
The remainders, read in reverse order, give the binary representation of 255: 11111111.
Similarly, to convert a binary number to decimal, you need to multiply each digit by its corresponding power of 2 and sum the results. For example, to convert the binary number 1101 to decimal:
1 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0 = 8 + 4 + 0 + 1 = 13
Here is a list of decimal numbers from 0 to 20:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
And here is a table of some commonly used decimal values and their equivalents in binary, octal, and hexadecimal:
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 3 | 11 | 3 | 3 |
| 4 | 100 | 4 | 4 |
| 5 | 101 | 5 | 5 |
| 6 | 110 | 6 | 6 |
| 7 | 111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 17 | 100 |
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