Tech+ (Episode 8): Notational Systems (1.2), Part 4

Hey everyone, welcome back to the CompTIA Tech+ series on krichardlabbe.com! I’m Kevin, and we’re keeping the number party going. Last time, we flipped decimal into binary with switches—super fun, right? Today, we’re tackling two more: decimal to octal and decimal to hex. No math meltdowns here—just simple steps, like packing boxes or picking paint colors. We’ll convert one number into both, so you’ll see how they work. Let’s roll!

We’re taking 20—yep, 20 bucks, 20 cookies, 20 tacos (my favorite) whatever—and turning it into octal and hexadecimal. By the end, you’ll be a pro at switching between these systems. Ready? Here we go!

Decimal to Octal - Packing by Eights

First up: Octal, that base-8 system with digits 0 to 7. Think of it like packing stuff into boxes that hold 8 each. We start with our number, 20, and figure out how many boxes of 8 we need, then what’s left over. The trick? Divide by 8 and keep track of the remainders.

So, 20 divided by 8 is 2—that’s two full boxes of 8. 2 times 8 is 16, and 20 minus 16 leaves 4. No more 8s fit into 4, so we’re done there. Write it like this:

• The 2 is how many 8s—put that first.
• The 4 is the leftovers—put that next.

That’s 24 in octal! Check it: 2 × 8 + 4 = 16 + 4 = 20. It matches! Octal just says, ‘Hey, I’ve got two groups of 8 and 4 extras.’

It’s like packing groceries—how many bags of 8, plus what’s still in your hands. Easy peasy!

Decimal to Hex

Now, Hexadecimal—base-16, with 0-9 and A-F, where A is 10, B is 11, up to F for 15. This is like picking bigger boxes that hold 16. Same deal: divide by 16 and see what’s left.

20 divided by 16 is 1—that’s one box of 16. 1 times 16 is 16, and 20 minus 16 is 4. No more 16s fit into 4, so we stop. Write it:

• The 1 is how many 16s.
• The 4 is what’s left—no letters needed, since 4 is still 4 in hex.

That’s 14 in hex! Check it: 1 × 16 + 4 = 16 + 4 = 20. Perfect! In hex, 14 means one group of 16 plus 4—same 20, just fancier.

Hex is cool because it’s compact—think of it like a shorthand for bigger numbers, perfect for tech stuff like color codes.

Take 1A3—it’s 1 group of 256, A (10) groups of 16, and 3 ones. That’s 256 + 160 + 3 = 419 in decimal. It’s like counting with 16 fingers—bigger steps each time!

Let’s try one more—25—just to lock it in.

• Octal: 25 ÷ 8 = 3 (three 8s). 3 × 8 = 24, 25 - 24 = 1. So, 31 in octal. Check: 3 × 8 + 1 = 25.
• Hex: 25 ÷ 16 = 1 (one 16). 1 × 16 = 16, 25 - 16 = 9. So, 19 in hex. Check: 1 × 16 + 9 = 25.

See the pattern? Divide by the base—8 for octal, 16 for hex—write the result, then the remainder. If hex’s remainder hits 10 or more, you’d use A, B, C—but 9’s still 9 here.

It’s like splitting candy into different-sized piles—same total, different packaging!

Wrapping It Up

There you go! Decimal to octal and hex is all about dividing by the base—8 or 16—and stacking the results. No crazy math—just divide, subtract, and write. You’re basically a number translator now!

Next time, we’ll flip some of these back—like octal or hex to binary—keeping it chill and step-by-step. You’re rocking this Tech+ prep, so hit that subscribe button, check out krichardlabbe.com for more, and drop a comment with a number you want to try. See you soon!

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