Tech+ (Episode 9): Notational Systems (1.2), Part 5

Hey everyone, welcome back to the CompTIA Tech+ series on krichardlabbe.com! I’m Kevin, and today we’re putting the final bow on our notational systems adventure. We’ve gone from decimal to binary, then to octal and hex—now it’s time to reverse it! 

We’re taking octal and hexadecimal numbers and turning them back into binary, those 0s and 1s computers love. No stress, no fuss—just a cool trick to unpack the boxes we packed last time. Let’s do this!

We’ll use numbers we’ve seen before: 24 in octal and 14 in hex—both are 20 in decimal. By the end, you’ll see how they both flip back to the same binary: 10100. Ready? Let’s start!

Octal to Binary

First, Octal to Binary. Octal is base-8, using digits 0 to 7, and it loves grouping binary digits into sets of three. So, to go back from octal to binary, we take each octal digit and turn it into a three-bit binary number—like unpacking little bundles of 0s and 1s.

Let’s take 24 in octal—that’s 20 in decimal, just so we’re on the same page. Split it into its digits: 2 and 4.

• 2 in binary? Picture our switches: 4, 2, 1. It’s 0 × 4 + 1 × 2 + 0 × 1 = 2. That’s 010.
• 4? Same deal: 1 × 4 + 0 × 2 + 0 × 1 = 4. That’s 100.
• Put them together: 010 100.

That’s 010100 in binary. 

Now, let’s check it with five bits to match 20: 0 × 16 + 1 × 8 + 0 × 4 + 1 × 2 + 0 × 1 = 8 + 2 = 10. 

Wait—20 needs one more bit! In binary, 20 is 10100: 1 × 16 + 0 × 8 + 1 × 4 + 0 × 2 + 0 × 1 = 20. So, octal 24 should align with 10100—yep, that’s it!"

Each octal digit gives you three bits, and for 20, we just read it as 10100. It matches perfectly—2 × 8 + 4 = 20 in decimal. Smooth and simple!

Each digit gets three bits—super consistent once you get the hang of it!

Hex to Binary

Now, Hex to Binary. Hex is base-16, with 0-9 and A-F, and it groups binary by fours. So, each hex digit becomes a four-bit binary chunk—like opening bigger bundles."

Take 14 in hex. Split it: 1 and 4.

• 1? Easy: 0 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 1. That’s 0001.
• 4? 0 × 8 + 1 × 4 + 0 × 2 + 0 × 1 = 4. That’s 0100.
  Combine them: 0001 0100.

That’s 00010100 in binary. Drop leading zeros if you want—it’s 10100. Check: 1 × 16 + 0 × 8 + 1 × 4 + 0 × 2 + 0 × 1 = 16 + 4 = 20. Matches perfectly—14 in hex is 20 in decimal!

Four bits per digit—hex makes it quick because it’s so compact!

Tying It Together

Look at that! Octal 24 and hex 14 both land on 10100 in binary, which is 20 in decimal. Octal unpacks by threes, hex by fours, but they’re just different wrappers for the same number in binary.

Wrapping It Up

And that’s the wrap on notational systems! We’ve gone from decimal to binary, to octal and hex, and now back again. Octal to binary? Three bits per digit. Hex to binary? Four bits. You’ve got the full circle now—converting any way you want, no math degree required. You’re becoming a Tech+ rockstar!

You’re making great progress for the FC0-U71 exam, so pat yourself on the back. Want more practice? Visit me on krichardlabbe.com, subscribe, and hit like! We’re onto bigger Tech+ adventures next, so stick around. See you soon!

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