🎮 Storytime: How Bit and Bot Discovered Binary

Once upon a techy time in a land not so far away, two curious bots, Bit and Bot, lived inside a giant computer. Every day, they worked hard flipping millions of tiny switches—some ON, some OFF. But here’s the twist: these weren’t ordinary switches. They were magical binary switches that powered everything in the digital world—from cat videos to video games!

One day, Bit asked Bot, “Why do we only use 0s and 1s? Why not 2s or 9s or even emojis?”

Bot grinned and replied, “Because we live in a binary world! In Binary Land, everything is either ON (1) or OFF (0)—just like our switches. That’s what computers understand best. It’s simple, fast, and perfect for our electronic brains!”

Bit nodded. “So, you’re saying that every photo, every song, every YouTube video is made up of just 0s and 1s?”

“Exactly!” said Bot. “That’s the magic of the binary number system!”

🔍 Let’s Break It Down: What is the Binary System?

Alright, fam, real talk: while we humans are out here counting with 10 fingers (hello, base-10/denary system ✋✋), computers only count using 2 fingers: 0 and 1.

This is because inside every computer, there are millions of teeny-tiny switches (called transistors). These switches are either:

  • ON (represented as 1)
  • OFF (represented as 0)

So, instead of counting like this:

Denary: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9...

Computers count like this:

Binary: 0, 1, 10, 11, 100, 101, 110, 111, 1000...

Each digit (or bit) in a binary number stands for a power of 2. So when you see a binary number like:

1 1 1 0 1 1 1 0

You’re actually looking at a coded message using the powers of 2! Here’s what it really means:

Binary Digit 1 1 1 0 1 1 1 0
Power of 2 128 64 32 16 8 4 2 1

Now just add up the values where there’s a 1:

128 + 64 + 32 + 8 + 4 + 2 = 238

Boom! Binary number 11101110 = 238 in denary.

🔁 Converting Backwards: From Denary to Binary

So, say you’ve got a number like 107, and you want to send it to Bit and Bot in their language (binary). How do you do it? You’ve got 2 main cheat codes:

💡 Method 1: Trial and Error (a.k.a. “Guess with Brains”)

You find the largest power of 2 less than or equal to the number, subtract, and keep going.

Example: Convert 107 Biggest power of 2 less than 107 is 64 → 107 – 64 = 43 Next biggest is 32 → 43 – 32 = 11 Next is 8 → 11 – 8 = 3 Next is 2 → 3 – 2 = 1 Next is 1 → 1 – 1 = 0 (Done!)

Now fill in the powers of 2 with 1s for the numbers you used, and 0s for the ones you skipped.

128  64  32 16  8  4  2  1
  0   1   1  0  1  0  1  1  → 01101011

🧠 Method 2: Successive Division by 2

This one’s smoother if you like patterns. You divide by 2 and write down the remainders, then read them from bottom to top.

Let’s do 107:

107 ÷ 2 = 53 R1  
 53 ÷ 2 = 26 R1  
 26 ÷ 2 = 13 R0  
 13 ÷ 2 = 6  R1  
  6 ÷ 2 = 3  R0  
  3 ÷ 2 = 1  R1  
  1 ÷ 2 = 0  R1

Now read remainders from bottom → top: 1101011

So, 107 = 1101011 in binary.

🧪 Practice Time with Bit and Bot!

Now that you’re a binary wizard 🧙‍♂️, let’s test those skills.

✍️ Review Questions:

  1. What does the binary number 10101010 equal in denary?
  2. Convert the denary number 156 to binary using the trial and error method.
  3. Why do computers prefer binary over denary?
  4. Convert this binary number to denary: 00010010
  5. Using the division method, convert 45 to binary.
<
Previous Post
01-Binary Systems and Hexadecimal: Unpacking the Binary Building Blocks of Computers
>
Next Post
🧙‍♂️ Python Sets: A Wizard’s Guide to Unordered Power