Hexadecimal Number System

Hexadecimal Number System

What you'll learn: How base-16 notation makes it easier to read and write binary values.

Why Hexadecimal Exists

You've been working with binary (base-2) and decimal (base-10). Binary is how computers think, but it gets unwieldy fast—imagine writing 11010110101111001010 every time! Hexadecimal (base-16) is a compact shorthand for binary that humans can actually work with.

How Hexadecimal Works

Hexadecimal uses 16 symbols to represent values:

• 0-9 for values zero through nine
• A-F for values ten through fifteen

Here's the mapping:

Decimal:  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15
Hex:      0  1  2  3  4  5  6  7  8  9   A   B   C   D   E   F

The Magic Connection to Binary

The beauty of hexadecimal is that one hex digit represents exactly four binary digits (bits). This is because 16 = 2⁴.

For example:

• Binary 1111 = Decimal 15 = Hex F
• Binary 1010 = Decimal 10 = Hex A
• Binary 0101 = Decimal 5 = Hex 5

To convert a longer binary number to hex, group it into chunks of four bits from right to left:

Binary 11010110 → Group as 1101 0110 → Hex D6

Think of hex as a compression format for binary—instead of writing 8 binary digits, you write 2 hex digits. Same information, far more readable!

Why Programmers Love Hex

When you see memory addresses, color codes (like #FF5733), or low-level data, they're usually in hexadecimal because it strikes the perfect balance: close to how computers work (binary) but compact enough for humans to read.

Key Takeaway: Hexadecimal (base-16) uses digits 0-9 and letters A-F, with each hex digit representing exactly four binary bits, making it a compact and readable way to work with binary data.