Once upon a time, in a place not far from your computer screen, there was a magical town called Bit Flip Town. In this town, every number had to wear a special jacket made up of 8 light switches. These tiny switches were called bits.

Each bit could either be:

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

These bits formed a number’s binary outfit — a code that told everyone exactly who that number was.

Now, here comes our hero — or should we say, our mischievous wizard — named Tilda. 🧙🏽‍♀️ She had one job: FLIP ALL THE BITS! That’s right. Every time someone passed by and shouted a number at her, she flipped their entire bit outfit — turning all 1s into 0s and all 0s into 1s.

Tilda’s favorite spell? You guessed it… the Bitwise NOT operator: ~

🧮 Tilda’s Magic: The ~ Spell

Every time you do ~x in JavaScript, here’s what happens:

💡 She turns x into -(x + 1)

It’s like taking the number, adding 1 to it, and making the answer negative!

Let’s visit a few villagers to see how Tilda changes their clothes…

🧙‍♀️ Tilda Flips the Town – One Bit at a Time

Here’s a table that shows what happens when the wizard Tilda casts her spell on each number:

Value (base 10) Binary Outfit 👕 Flipped Outfit 🧥 Final Result 🎯
2 00000010 11111101 -3
1 00000001 11111110 -2
0 00000000 11111111 -1
-1 11111111 00000000 0
-2 11111110 00000001 1
-3 11111100 00000010 2

🕵🏽 Let’s Sneak into Each Wardrobe

🧢 1. The Boy Named “2”

He wore a jacket like this: 00000010 Only one light was ON — the third from the right.

Tilda came along, said “Flip!”, and ZAP! — it became: 11111101 Now everyone called him -3 because:

~2 = -(2 + 1) = -3

🧢 2. The Little One — “1”

Original outfit: 00000001 Flip it and boom 💥 → 11111110 Which means:

~1 = -(1 + 1) = -2

🧢 3. The Baby “0”

Outfit: 00000000 — No lights ON! After the flip: 11111111 — All lights turned ON! Which is JavaScript’s way of saying:

~0 = -(0 + 1) = -1

🧢 4. Mister Grumpy “-1”

Outfit: 11111111 — All lights ON. After Tilda flipped it: 00000000 — All OFF! And guess what?

~(-1) = -(-1 + 1) = 0

🧢 5. Old Man “-2”

He came in with 11111110 Flip that → 00000001 Which means:

~(-2) = -(-2 + 1) = 1

🧢 6. Uncle “-3”

Wearing: 11111100 Tilda flipped him into: 00000010 And that’s 2 in disguise!

~(-3) = -(-3 + 1) = 2

🎩 The Secret Rule of Tilda’s Spell

Whenever you see ~x, just remember this simple formula:

💫 ~x = -(x + 1)

That’s how JavaScript plays this bit-flipping magic trick!

🎨 See It Again in Colorful Costumes

Here’s a recap for your comic-style notes:

🧍 Number 👕 Binary Outfit 🧥 Tilda’s Flip 🎯 Final Answer
2 00000010 11111101 -3
1 00000001 11111110 -2
0 00000000 11111111 -1
-1 11111111 00000000 0
-2 11111110 00000001 1
-3 11111100 00000010 2

✍🏽 Time to Practice in Bit Flip Town!

Let’s see how much of a wizard YOU are now! 🧙🏽‍♂️

🎯 Practice Questions:

  1. If you give Tilda the number 4, what do you think she returns? (Hint: Use the rule ~x = -(x + 1))

  2. What is the binary of 3? What does it become when Tilda flips it?

  3. Why does ~0 always return -1 in JavaScript?

  4. Use the rule to find: What is ~(-5)?

  5. If a binary number looks like 11111110, what was the original number before the flip?

🎁 Bonus Challenge:

Write a JavaScript line that uses the bitwise NOT to check if a number is zero or not?

let x = 0;
if (~x) {
  console.log("Not zero!");
} else {
  console.log("It’s zero!");
}
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