Yo, welcome to another coding campfire tale! 🔥 Today, we’re diving into how to convert a denary number (that’s a fancy word for normal numbers like 107) into the secret language of computers — binary (only 1s and 0s, baby 😎).

And guess what? There are two chill ways to get it done:

  • The “Trial and Error” way — like playing a matching game.
  • The “Successive Division” way — like flipping a bunch of coins.

So grab your hoodie, crack your knuckles, and let’s turn 107 into binary like a total boss.

🚀 Method 1: Trial and Error (The Coin Collector Game 🎮)

Imagine you’re at a secret gamer shop that only sells coins in powers of 2:

  • 1, 2, 4, 8, 16, 32, 64, 128…

You need to buy exactly 107 coins using the biggest possible values without going over. Let’s goooo:

  • 64 fits into 107 → Remaining = 43 → Put a 1 under 64
  • 32 fits into 43 → Remaining = 11 → Put a 1 under 32
  • 16 is too big for 11 → Put a 0
  • 8 fits → Remaining = 3 → Put a 1
  • 4 is too big → Put a 0
  • 2 fits → Remaining = 1 → Put a 1
  • 1 fits → Remaining = 0 → Put a 1

Here’s your binary lineup:

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

So, 107 in binary = 1101011 ✨ Boom, you just built 107 using binary blocks!

🧮 Method 2: Successive Division by 2 (The Stack & Flip Trick 🔄)

This one’s all about dividing by 2 and catching the remainders like Pokémon.

Let’s divide 107 down till we hit zero:

  1. 107 ÷ 2 = 53 — remainder 1
  2. 53 ÷ 2 = 26 — remainder 1
  3. 26 ÷ 2 = 13 — remainder 0
  4. 13 ÷ 2 = 6 — remainder 1
  5. 6 ÷ 2 = 3 — remainder 0
  6. 3 ÷ 2 = 1 — remainder 1
  7. 1 ÷ 2 = 0 — remainder 1

Now reverse the remainders (from bottom to top): 1 1 0 1 0 1 1

So, 107 in binary = 1101011 again. 🔥 We’re on fire, and we didn’t even need Wi-Fi to do it!

🧠 Recap

  • Computers speak binary (just 1s and 0s).
  • Denary = regular numbers like 107.

  • Use:

    • Trial and Error: Build the number using powers of 2.
    • Successive Division: Keep dividing by 2, then read remainders bottom to top.
  • Either way, 107 = 1101011 in binary.

Test Your Brain Juice

Let’s see if you’re the next binary beast 👾

  1. Use Trial and Error to convert 85 to binary.
  2. Use Successive Division to convert 42 to binary.
  3. What’s the value of the 5th digit from the right in a binary number?
  4. Which method do you prefer and why?
  5. Convert 15 to binary using both methods. Do you get the same result?
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