Tech+ (Episode 6): Notational Systems (1.2), Part 2

Hey everyone, welcome back to my CompTIA Tech+ series! I’m Kevin, and today we’re picking up where we left off with notational systems. Last time, we met binary—those 0s and 1s computers love—and today, we’re going to turn them into something we humans can understand: decimal, octal, and hexadecimal. Don’t panic if math makes you nervous—this is going to be as easy as flipping a light switch. Let’s get started!

Binary’s the computer’s language (we might say love language!)—0 for off, 1 for on. But how do we switch it to decimal, octal, or hex? We’re going to take one binary number, 1010, and convert it to all three. By the end, you’ll see it’s less about math and more about patterns. Ready? Let’s go!

Binary to Decimal

First up: Binary to Decimal—that’s our everyday 0-9 system. Here’s how it works. Each spot in a binary number is like a switch with a value, starting from the right. The rightmost spot is worth 1, the next is 2, then 4, then 8, doubling each time, and so on. If the switch is on—1—you count that value. If it’s off—0—you skip it.

So, take 1010. From right to left:

• First spot: 0 × 1 = 0. Off, so nothing.
• Second: 1 × 2 = 2. On, so we get 2.
• Third: 0 × 4 = 0. Off, nada.
• Fourth: 1 × 8 = 8. On, so 8.
• Add them up: 0 + 2 + 0 + 8 = 10. That’s it—1010 in binary is 10 in decimal!

It’s like counting how many lights are on in a row. No big equations—just add the ‘on’ spots. Easy, right?

Binary to Octal

Next: Binary to Octal, that base-8 system with 0-7. Here’s the trick: group your binary digits into sets of three, starting from the right. Since 1010 is short, we add zeros on the left to make it work—think of it like padding a sandwich. So, 1010 becomes 001010."

Now, each group of three turns into one octal digit:

• 001: That’s 0 × 4 + 0 × 2 + 1 × 1 = 1.
• 010: That’s 0 × 4 + 1 × 2 + 0 × 1 = 2.
• Put them together: 12 in octal!

12 in octal means 1 eight and 2 ones, which is 10 in decimal—same as before! It’s like bundling sticks into piles of eight. 

I know, I know - if you’re not a math person, this can seem a little nutty. Trust me: it will come together the more you dabble with it. If I can do it, you certainly can - believe me. 

We’ll double-check these conversions in another video, but this is the quick way.

Binary to Hex

Last one: Binary to Hexadecimal, base-16 with 0-9 and A-F. This time, group by fours from the right. 1010 is already four digits, so no padding needed."

Turn it into one hex digit:

• 1010 is 1 × 8 + 0 × 4 + 1 × 2 + 0 × 1 = 8 + 0 + 2 + 0 = 10.
• In hex, 10 is written as A—because A is 10, B is 11, up to F for 15. So, 1010 in binary is A in hex!"

A in hex is 10 in decimal—matches again! Hex loves groups of four because it’s a shortcut for binary in tech, like those color codes on websites.

Wrapping It Up

There you go! Binary 1010 becomes 10 in decimal, 12 in octal, and A in hexadecimal. It’s all about spotting the pattern:

• Decimal adds up the ‘on’ switches—8, 4, 2, 1.
• Octal groups by threes and counts to 7.
• Hex groups by fours and goes all the way to F.

See? No math degree needed—just a little practice!"

Want more? Next time, we’ll flip it around—decimal to binary, octal to hex, all that jazz. It’s step-by-step, no stress, I promise. You’ll get it.

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