Hexadecimal, often abbreviated as “hex,” is a numeral system that uses a base of 16. It is commonly used in computing and mathematics to represent binary data and memory addresses more concisely. Hexadecimal digits range from 0 to 9, followed by the letters A to F, where A represents 10, B represents 11, and so on up to F, which represents 15.
In the hexadecimal system, each digit represents a value that is a power of 16. The rightmost digit represents the ones place, the next digit to the left represents the 16s place, the next represents the 256s (16^2) place, and so on. The value of a digit in hexadecimal is calculated by multiplying the digit by the corresponding power of 16.
Here is a table showing the decimal, binary, and hexadecimal representations of numbers from 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 |
To convert a number from binary or decimal to hexadecimal, you divide the number by 16 repeatedly and note the remainder at each step. The remainders are then assigned hexadecimal digits from right to left.
For example:
- To convert the binary number 10110101 to hexadecimal, group the binary digits into sets of four (from right to left): 1011 0101. Each set can be converted to a hexadecimal digit: B 5. Therefore, the hexadecimal representation of 10110101 is B5.
- To convert the decimal number 187 to hexadecimal, divide 187 by 16, which results in a quotient of 11 and a remainder of 11. The remainder 11 corresponds to the hexadecimal digit B. The quotient 11 is less than 16, so it can be directly represented as the hexadecimal digit 11. Therefore, the hexadecimal representation of 187 is BB.
Hexadecimal is commonly used in various computing contexts, such as representing memory addresses, color values in graphics, and encoding binary data. It provides a concise and human-readable representation of binary values while being easily convertible to and from binary and decimal representations.
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