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DEMO: Counting in Hexadecimal

Hexadecimal counting follows the same positional logic as decimal and binary, using the letters A through F to represent values ten through fifteen before resetting and carrying to the next column.

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About this video

Hexadecimal is a base-16 numbering system widely used in computing, networking, and cybersecurity contexts such as memory addressing, color codes, and cryptographic output. Like decimal and binary, it relies on positional notation, meaning each column represents a power of 16. Where decimal uses digits zero through nine and binary uses only zero and one, hexadecimal extends the digit set by assigning the letters A through F to the values ten through fifteen, allowing a single character to represent any value in that range without ambiguity. Counting in hexadecimal proceeds normally from zero through nine, then continues as A, B, C, D, E, and F before the column resets to zero and a one is carried to the next position. The same carry logic applies across all columns, so moving from 1F to 20, or from AF to B0, follows the same mechanical process as crossing any column boundary in decimal arithmetic. Practicing with short sequences and identifying the next value in a series is an effective way to build fluency and avoid errors when working with hex values in real-world IT and security tasks.

What you'll learn

What's covered

Counting in Hexadecimal

Aligned to

CompTIA Tech+
1.1 Compare and contrast notational systems.

Key terms

Hexadecimal
Hex
A base-16 number system using digits 0–9 and letters A–F; each hex digit maps to exactly 4 bits, making it a compact shorthand for representing binary data.
Base-16
Another name for the hexadecimal numbering system, where each digit position represents a power of 16.
Digit Rollover
The reset of a column back to zero once it reaches its maximum value, triggering a carry to the next column.
Carry
In binary addition, the value of 1 passed to the next higher bit position when a column's sum exceeds the maximum value representable by a single bit.

Transcript

Counting in Hexadecimal

We're going to go over counting in hexadecimal, and we're going to jump right into it. One of the best ways to learn something is to jump in and just start doing it, so that's what I'm going to challenge you to do here in a little bit. But before we do that, I'm going to give you a little bit of instruction.

Number one: what we're doing here is really no different than in binary numbers or with the decimal system. I've shown you how to use those numbering charts; use the same one here and the same concepts to fill this out.

The other thing is, if we have a single column here, we can represent zero, one, two, three, four, five, six, seven, eight, nine fairly easily and count up that way. But once we hit 10, that takes two digits in decimal. So instead of writing out 10, we would do A. Instead of 11, that would be B; 12 would be C; 13, D; 14, E; 15, F. I've got that all written here. And then of course don't forget to reset that column and carry something over to the next column.

So go ahead and go through this process. Try counting in hexadecimal and see how well you can do with just the little instruction that I've given you so far.

Working Through the Count

Here's the answer to check your work. Go ahead and check it out and see how well you did, and then we'll discuss what this looks like in case you have any questions.

To count with this, again, we're going to start with zero, one, two, three, four, five, six, seven, eight, nine. That's all pretty much straightforward and follows the decimal system, so nothing too different there. And then, if you figured it out, you go into those numbers A, B, C, D, E, F. Once we get to F, that represents all 16, 0 through 15, numbers here for this first column. We would reset this and carry one over to the next column, so now we're at one on the next column, and then we go through that process all over again: 11, 12, 13, and so on and so forth. So that's how to do hexadecimal numbers, and how to count in hexadecimal.

An Exercise

Here's an exercise to further test your knowledge. Go ahead and go through here and figure out what the next number is for each of these sequences, and then you can check your answers.

Here are the answers. Check your work, see how well you did, and then I'll run through all of these in case you have any questions. I'll go ahead and go through all of this process just in case you have any questions.

  • If I were to take the hexadecimal number 23 and add 1 to it, that would be 24. It's pretty straightforward.
  • Same thing with this A1: adding one to it, it just becomes A2.
  • If we add 1 to DE, that becomes a little more interesting, but it's still not that far off, because the next thing that comes after E is F, so that is DF.
  • AF gets a little bit more tricky, because if we're going to add 1 to it, what we do is we reset that first column and that becomes a zero, we carry a one to the next column and that becomes a B, so we end up with B0 for that one.
  • 19: the next one would be 1A, because what comes after 9 is A. So that could get a little tricky.
  • FD: so the next one is FE.
  • 3F: we add one to that, the F becomes a zero, we carry the one, and that becomes 40.
  • And then 89: we add one to that and it becomes 8A.

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