There lived a crew of numbers who only spoke in 0s and 1s. Yep, that’s right—just two digits. They were super disciplined. No drama. No extra numbers. Just chillin’ with either a 0 or a 1.

Now, their neighboring kingdom—Denary-Land (you know, where we count from 0 to 9, like normal humans)—was like, “Hey, how do we understand these binary peeps?”

That’s where the magic of conversion came in! ✨

🎯 So, What’s the Big Idea?

Binary is based on powers of 2, while denary (aka base 10) is based on powers of 10. So instead of thinking:

  • Ones place = 1
  • Tens place = 10
  • Hundreds = 100 and so on…

Binary thinks:

  • First spot = 2⁰ (that’s 1)
  • Next = 2¹ (that’s 2)
  • Next = 2² (that’s 4)
  • Then 8, 16, 32, 64, 128…

It’s like a row of power-ups in a game. And the ‘1’ means you pick up the power, the ‘0’ means you skip it.

🎮 The Example: Binary Code 11101110

Let’s pretend this is a secret code from a robot: 1 1 1 0 1 1 1 0

Let’s give them their superpower positions:

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

Now follow this rule: If it’s a 1, you add the value. If it’s 0, ignore it.

So, we add up:

  • 128 ✅
  • 64 ✅
  • 32 ✅
  • 16 ❌ (skipped because it’s 0)
  • 8 ✅
  • 4 ✅
  • 2 ✅
  • 1 ❌ (skip again)

Now let’s add it like we’re at a checkout counter:

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

Boom! 💣 You just cracked the binary code like a real tech ninja.

🧠 Let’s Wrap It Up in One Line:

“Each ‘1’ in binary is like turning ON a power switch, and every switch gives you a different number. Add the ones that are ON, and you get the denary version.”

✍🏽 Your Turn! Practice Time

Okay boss, let’s see what you got. Try these and flex those brain muscles:

  1. Convert this binary number to denary: 1 0 1 0 1 0 1 0
  2. Convert this to denary: 0 1 1 1 0 0 1 1
  3. What would be the 5th power of 2 in the binary headings?
  4. If a binary number has all 1s (like 11111111), what’s its denary value?
  5. True or False: In binary, 2⁴ is the same as the 5th column from the right.
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