The hexadecimal number 255 represents the decimal value 653 because each hexadecimal digit corresponds to four binary digits. In hexadecimal, 2 is 0010 in binary, 5 is 0101 in binary, and 5 is 0101 in binary. Combining these gives 001001010101 in binary, which translates to decimal 653.

Understanding Hexadecimal: Why 255 Isn’t What You Might Expect

You’ve likely encountered the number 255 in computing contexts, often associated with maximum values or color codes. However, when you see 255 represented in hexadecimal, it doesn’t directly translate to the decimal number 255. This might seem confusing at first, but understanding how hexadecimal works reveals the logic behind these representations.

What is Hexadecimal?

Hexadecimal, often shortened to "hex," is a base-16 numbering system. Unlike our familiar decimal system (base-10), which uses ten digits (0-9), hexadecimal uses sixteen symbols. These symbols are the digits 0-9 and the letters A-F. Each letter represents a decimal value: A=10, B=11, C=12, D=13, E=14, and F=15.

This system is widely used in computing because it offers a more human-readable way to represent binary code. Binary, the language of computers, uses only two digits (0 and 1). Hexadecimal provides a compact shorthand for these long strings of ones and zeros.

Decoding the Hexadecimal Number 255

Let’s break down the hexadecimal number 255 (often written as 0x255 or 255h to denote it as hexadecimal).

• The first digit is ‘2’. In hexadecimal, ‘2’ directly corresponds to the decimal value 2.
• The second digit is ‘5’. In hexadecimal, ‘5’ directly corresponds to the decimal value 5.
• The third digit is ‘5’. Again, in hexadecimal, ‘5’ directly corresponds to the decimal value 5.

Now, to convert this hexadecimal number to its decimal equivalent, we use place values. In a base-16 system, each position represents a power of 16. Starting from the rightmost digit:

• The rightmost ‘5’ is in the $16^0$ (or $16^0$) place.
• The middle ‘5’ is in the $16^1$ (or $16^1$) place.
• The leftmost ‘2’ is in the $16^2$ (or $16^2$) place.

So, the calculation is:

$(2 \times 16^2) + (5 \times 16^1) + (5 \times 16^0)$

Let’s compute this:

$(2 \times 256) + (5 \times 16) + (5 \times 1)$

$512 + 80 + 5$

This equals 605.

Therefore, the hexadecimal number 255 is equivalent to the decimal number 605.

Why the Confusion with Decimal 255?

The common confusion arises because the decimal number 255 is a significant value in computing, particularly in 8-bit systems. For example, in an 8-bit unsigned integer, the maximum value you can represent is $2^8 – 1 = 256 – 1 = 255$. This is also the maximum value for each individual Red, Green, or Blue (RGB) color channel in many digital formats (like web colors), where values range from 0 (no intensity) to 255 (full intensity).

When people see FF in hexadecimal, they often associate it with this maximum value. This is because FF in hexadecimal is indeed equal to decimal 255.

• ‘F’ in hex is 15 in decimal.
• So, FF (hex) is $(15 \times 16^1) + (15 \times 16^0) = (15 \times 16) + (15 \times 1) = 240 + 15 = 255$ (decimal).

This is why you’ll frequently see 255, 255, 255 for white or 0, 0, 0 for black in RGB color codes, and their hexadecimal equivalents are #FFFFFF and #000000, respectively.

Hexadecimal vs. Decimal: A Quick Comparison

To further clarify, let’s look at how some numbers translate between systems.

Decimal	Hexadecimal	Explanation
10	A	‘A’ is the hex symbol for decimal 10.
16	10	One ’16’ and zero ‘1’s in base-16.
255	FF	Fifteen ’16’s and fifteen ‘1’s ($15 \times 16 + 15 \times 1$).
256	100	One $16^2$, zero $16^1$s, and zero $16^0$s ($1 \times 256 + 0 \times 16 + 0 \times 1$).
605	255	Two $16^2$s, five $16^1$s, and five $16^0$s ($2 \times 256 + 5 \times 16 + 5 \times 1$).

Why is Hexadecimal So Important in Tech?

Hexadecimal’s prevalence in technology stems from its efficient representation of binary data.

• Readability: It’s much easier for humans to read and write FF0000 than 111111110000000000000000.
• Compactness: Each hex digit represents exactly four binary digits (a nibble). This makes it a perfect bridge between the binary world of computers and the decimal world of humans.
• Memory Addresses: Hexadecimal is commonly used to display memory addresses, register values, and raw data in debugging and programming.
• Color Codes: As mentioned, RGB color values are often expressed in hex (e.