Hexadecimal is a number system that uses 16 symbols to represent numbers, including the digits 0-9 and the letters A-F. Each hexadecimal digit represents a value from 0 to 15, allowing for easy conversion to binary and decimal systems.
In hexadecimal, the first 10 symbols represent the values 0 to 9, while the letters A to F represent values 10 to 15. The letter 'A' represents the value 10, 'B' represents 11, 'C' represents 12, 'D' represents 13, 'E' represents 14, and 'F' represents 15.
To convert a hexadecimal number to decimal, each digit is multiplied by the corresponding power of 16 and the results are added together. For example, the hexadecimal number 2F6 can be converted to decimal as follows:
2F6 = (2 x 16^2) + (15 x 16^1) + (6 x 16^0)
= (2 x 256) + (15 x 16) + (6 x 1)
= 512 + 240 + 6
= 758
To convert a decimal number to hexadecimal, the decimal number is repeatedly divided by 16 until the quotient is zero, and the remainders are used as the hexadecimal digits. The remainders are listed in reverse order to obtain the hexadecimal representation of the decimal number. For example, the decimal number 758 can be converted to hexadecimal as follows:
758 / 16 = 47 remainder 6
47 / 16 = 2 remainder 15 (which is F in hexadecimal)
2 / 16 = 0 remainder 2
Therefore, 758 in decimal is equivalent to 2F6 in hexadecimal.
Here is a table showing the decimal, binary, and hexadecimal values for the numbers 0 to 15:
| Decimal | Binary | Hexadecimal |
|---|---|---|
| 0 | 0000 | 0 |
| 1 | 0001 | 1 |
| 2 | 0010 | 2 |
| 3 | 0011 | 3 |
| 4 | 0100 | 4 |
| 5 | 0101 | 5 |
| 6 | 0110 | 6 |
| 7 | 0111 | 7 |
| 8 | 1000 | 8 |
| 9 | 1001 | 9 |
| 10 | 1010 | A |
| 11 | 1011 | B |
| 12 | 1100 | C |
| 13 | 1101 | D |
| 14 | 1110 | E |
| 15 | 1111 | F |
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