The hexadecimal representation of the decimal number 255 is FF.
Understanding Hexadecimal and Decimal Numbers
To grasp why 255 translates to FF, it's essential to understand the different number systems involved:
- Decimal (Base-10): This is the everyday number system we use, employing ten unique digits (0-9). Each position in a decimal number represents a power of 10.
- Hexadecimal (Base-16): This system uses sixteen unique symbols. It includes the standard ten digits (0-9) and the first six letters of the alphabet (A-F) to represent values from ten to fifteen. Hexadecimal numbers are commonly used in computing and digital electronics because they offer a more compact way to represent binary data. For more details on this system, you can refer to the Wikipedia page on Hexadecimal.
Converting Decimal 255 to Hexadecimal
Converting a decimal number to hexadecimal typically involves repeatedly dividing the decimal number by 16 and recording the remainders.
Step-by-Step Conversion
Here's how to convert 255 from decimal to hexadecimal:
- First Division: Divide 255 by 16.
- $255 \div 16 = 15$ with a remainder of $15$.
- In hexadecimal, the digit
15is represented by the letter F. This is the rightmost (least significant) digit of our hexadecimal number.
- Second Division: Take the quotient from the previous step (15) and divide it by 16.
- $15 \div 16 = 0$ with a remainder of $15$.
- Again, the digit
15is represented by the letter F. This is the next digit to the left.
- Final Result: Read the remainders from bottom to top. The remainders are F and F, giving us FF.
This conversion clearly shows that 255 in decimal is equivalent to FF in hexadecimal. This value is particularly significant as it represents the maximum value that can be stored in an 8-bit unsigned integer (where each 'F' corresponds to four binary ones, making FF equivalent to eight binary ones: 11111111).
Significance of 255 and FF Across Bases
The number 255 holds a unique significance in various number systems, especially in digital contexts. As a repdigit (a number consisting of repeated identical digits), it showcases fascinating patterns:
- In base 2 (binary), 255 is
11111111. - In base 4, 255 is
3333. - And as established, in base 16 (hexadecimal), it is FF.
This characteristic makes 255 a frequently encountered value in computing.
Number Representation Comparison
The table below illustrates the representation of the number 255 across different bases:
| Base | Representation |
|---|---|
| Decimal | 255 |
| Binary | 11111111 |
| Hexadecimal | FF |
| Base 4 | 3333 |
Practical Applications of FF (Decimal 255)
The value FF (255) is not just a theoretical conversion; it has widespread practical applications in various fields of technology:
- Color Codes: In web development and graphic design, colors are often represented using RGB (Red, Green, Blue) values, where each component ranges from 0 to 255. For instance, pure white is represented as
(255, 255, 255), which translates to#FFFFFFin hexadecimal, indicating the maximum intensity for all three color channels. - Network Addressing (IPv4): In the Internet Protocol version 4 (IPv4), each of the four octets in an IP address (e.g.,
192.168.1.1) can range from 0 to 255. This maximum value is a direct consequence of each octet being an 8-bit number. - Bitwise Operations: Programmers often encounter 255 (
0xFFin many programming languages) when working with bitmasks, especially for operations that involve setting or clearing all bits within a byte.
