Imagine you’re invited to a super fancy party thrown by someone called “Hex” (short for Hexadecimal). Now, Hex is not your regular host. They don’t just invite 10 friends like the denary system (0 to 9) or 2 like the binary system (0 and 1). Nah, Hex goes hard and invites 16 friends 😮.

Hex’s guest list looks like this:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

But plot twist! The guests A to F are not your everyday names. Each of them has a secret identity:

  • A = 10
  • B = 11
  • C = 12
  • D = 13
  • E = 14
  • F = 15

So Hex throws a Base-16 bash 🎉 while Denary is stuck at Base-10 and Binary is doing a 0-and-1 dance.

🧠 Binary and Hex: BFFs Forever 👯

Okay, here’s a superpower secret: Hex and Binary are tight besties. Wanna know why?

Because 16 = 2⁴ — that’s four binary digits per one hex digit. It’s like saying:

Every time Hex writes one digit, Binary writes four.

Here’s how it rolls:

Hex Binary
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
A 1010
B 1011
C 1100
D 1101
E 1110
F 1111

So, if Binary writes 101111100001, Hex just casually says, “That’s BE1.” 😎

🔄 Conversions: Changing Forms Like a Transformer 🤖

🚀 Binary → Hex

Just:

  1. Group into 4 bits from the right.
  2. Add zeros to the left if needed.
  3. Use the table to match binary groups to Hex.

Example:

Binary: 101111100001
Groups: 1011 1110 0001
Hex:    B    E    1

🧩 Hex → Binary

Just reverse the magic:

  • Take each hex digit.
  • Convert it into a 4-bit binary chunk.

Example:

Hex: 45A
Binary: 0100 0101 1010

💥 Hex → Denary

Here’s the plan:

  • Multiply each digit by powers of 16.
  • Add ‘em up!

Example:

Hex: 45A
= (4 × 16²) + (5 × 16¹) + (A × 16⁰)
= (4 × 256) + (5 × 16) + (10 × 1)
= 1024 + 80 + 10 = **1114**

🔁 Denary → Hex

Two options:

Method 1: Trial and Error Like solving a puzzle. Break it into 16s, find digits.

Method 2: Repetitive Division

  1. Keep dividing the number by 16.
  2. Write the remainders.
  3. Read from bottom to top.

Example: 2004 ÷ 16 → remainder 4 125 ÷ 16 → remainder 13 (D) 7 ÷ 16 → remainder 7

So 2004 = 7D4 in Hex.

🎯 Real-Life Hex Heroes

💻 Memory Dumps

When things go boom 💥 in programs, developers look at memory dumps (like a computer’s brain scan) written in Hex. Wayyyy easier than long binary strings!

🎨 HTML Colors

You know colors on websites? They’re Hex-coded! Like:

  • 🔴 Red → #FF0000
  • 🟢 Green → #00FF00
  • 🔵 Blue → #0000FF

Mix ‘em up to get wild colors like #FF00FF (fuchsia 💅).

🌐 MAC Addresses

These are like your device’s fingerprint. MAC addresses use Hex too. Format: NN:NN:NN:DD:DD:DD Example: 00:1C:B3:4F:2D:E2

🧙‍♂️ Web Addresses (ASCII in disguise)

Sometimes websites use Hex in their URLs to look cooler or more secure: www.hodder.co.uk → %77%77%77%2E%68%6F...

🧬 Assembly & Machine Code

Programmers use Hex to avoid brain-frying binary when writing low-level code. Instead of this:

10100101111001001111111110100100

You write this:

A5E4 FFA4

Much easier, right?

✅ Review & Practice Time!

  1. What’s the Hex equivalent of the binary number 11010110?
  2. Convert the Hex number 2F to binary.
  3. Turn the Hex number 1A3 into denary.
  4. Convert the denary number 350 into Hex.
  5. Why is Hex easier for programmers than binary?
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