Tech+ (Episode 7): Notational Systems (1.2), Part 3

Hey there, welcome back to the CompTIA Tech+ series on krichardlabbe.com! I’m Kevin, and today we’re flipping the script—literally! Last time, we turned binary into decimal, octal, and hex. Now, we’re going the other way: taking a decimal number—like the ones we use every day—and turning it into binary, those 0s and 1s computers adore. If math makes you sweat, don’t worry—this is more like a game than a test. Let’s flip some switches and get started!

We’re going to convert 10 in decimal—that’s ten apples, ten bucks, whatever—into binary. By the end, you’ll see it’s just about breaking it down into little yes-or-no steps. Ready? Here we go!

The Binary Switch Trick

Remember how binary works? It’s base-2, just 0s and 1s, like switches—off is 0, on is 1. Each spot has a value that doubles from right to left: 1, 2, 4, 8, and so on. To turn decimal into binary, we figure out which switches need to be ‘on’ to add up to our number. It’s like picking the right coins to make a dollar—except here, it’s powers of 2.

So, we’ve got 10. We’ll use these spots: 8, 4, 2, 1. The question is: which ones do we turn on to get 10? Let’s work it out step-by-step.

Start with the biggest number that fits into 10 without going over. That’s 8.

• 10 minus 8 is 2. So, the 8 switch is on—write a 1 there.
• Next, can 4 fit into 2? Nope, 4’s too big. So, the 4 switch is off—write a 0.
• What about 2? Perfect—2 fits into 2 exactly. Switch on, write a 1.
• Now we’re at 0 (2 minus 2). Does 1 fit? No, we’re done—switch off, write a 0."

Now, let’s read it left to right: 1010. That’s binary for 10! Let’s check: 1 × 8 + 0 × 4 + 1 × 2 + 0 × 1 = 8 + 2 = 10. Boom—it works!

See? It’s like asking, ‘Can I use this big piece? No? How about this one?’ until you’ve got it all covered.

Let’s try one more—say, 5 in decimal. Same deal:

• 8’s too big—off, 0.
• 4 fits into 5—on, 1. 5 minus 4 is 1.
• 2’s too big for 1—off, 0.
• 1 fits into 1—on, 1. 1 minus 1 is 0, done."

That’s 0101. Check it: 0 × 8 + 1 × 4 + 0 × 2 + 1 × 1 = 4 + 1 = 5. Nailed it! The leading zero doesn’t change the value—it’s still 5—just like 5 and 05 are the same.

It’s all about finding the combo of 8s, 4s, 2s, and 1s that adds up to your number. No fancy formulas—just subtraction and switches!

Wrapping It Up

There you have it! Decimal to binary is just picking the right switches—start with your number, subtract the biggest power of 2 that fits, keep going till you’re at zero, and write 1s for ‘on,’ 0s for ‘off.’ 10 becomes 1010, 5 becomes 0101. It’s like a treasure hunt with only two answers: yes or no!

Next up, we’ll tackle decimal to octal and hex—same vibe, different twists. You’re crushing this Tech+ prep, so hit subscribe below, swing by krichardlabbe.com for more, and let me know in the comments if you want to try another number together. Catch you in the next one!

Every effort has been made to ensure the accuracy and reliability of the information presented in this material. However, Labbe Media, LLC does not assume liability for any errors, omissions, or discrepancies. The content is provided for informational and educational purposes only and should not be considered professional advice. Viewers are encouraged to verify any information before making decisions or taking actions based on it.

CompTIA and all associated trademarks, including logos and images, are the property of CompTIA, Inc. The use of any CompTIA logo in these materials is in accordance with CompTIA's brand and trademark guidelines. These materials are not sponsored, endorsed, or affiliated with CompTIA, Inc., and all opinions expressed are solely my own. For more information about CompTIA, please visit www.comptia.org.