🎨 Hexadecimal (Base 16)

📖 How Hexadecimal Works

Hexadecimal (or "hex") is base 16 — it uses 16 digits. Since we only have 10 number digits (0–9), we use letters for the extra six:

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

🎮 Where Hex Is Used

🎮 Hex in the Real World

Use	Example	Explanation
Colours	`#FF5733`	Red=FF (255), Green=57 (87), Blue=33 (51). Every colour on screen is hex.
Memory addresses	`0x7FFF5B2A`	RAM locations are shown in hex because it is shorter than binary
MAC addresses	`A4:83:E7:2F:01:BC`	Network card identifiers use hex pairs
Error codes	`0xDEADBEEF`	Famous debug value used by programmers (yes, really!)

🔍 Why Hex? It Compresses Binary

Each hex digit represents exactly 4 binary bits. This makes conversion simple:

Hex	F	F	5	7	3	3
Binary	1111	1111	0101	0111	0011	0011

So #FF5733 in binary would be 111111110101011100110011 — 24 digits instead of 6! Hex is just a compact way for humans to read binary.

🐍 Hex in Python

🐍 Hexadecimal in Python

# Python understands hex with the 0x prefix
red_value = 0xFF      # 255 in decimal
green_value = 0x57    # 87 in decimal
blue_value = 0x33     # 51 in decimal

print("Colour #FF5733 breakdown:")
print("  Red:  ", red_value)
print("  Green:", green_value)
print("  Blue: ", blue_value)

# Convert between systems
print()
number = 255
print(f"Decimal {number}:")
print(f"  Binary: {bin(number)}")
print(f"  Hex:    {hex(number)}")
print()
print(f"Decimal 1000 in hex: {hex(1000)}")
print(f"Hex 0x1A in decimal: {0x1A}")

🎯 Exam Tip

Hex digits A–F = decimal 10–15. Each hex digit = exactly 4 bits. So 1 byte (8 bits) = exactly 2 hex digits. The max value of 1 byte is FF in hex = 11111111 in binary = 255 in decimal.