What is a Hexadecimal? - Definition & Conversion

Instructor: Mark Boster
We use a base-ten system to count and solve math problems. However, if you would like to program computers, you need to learn about hexadecimals, a number system based on sixteen.

What Are Hexadecimals?

Computer scientists create the computer systems that you use to surf the net, play games online, and even read online lessons like these. And they program computers using a number system called hexadecimal.

A hexadecimal is a number system based on the number sixteen. To remember this, remember that hexa means six (like how a hexagon has six sides), and decimal refers to a system based on the number ten. And what do you get when you add six and ten? Sixteen!

So, instead of having only ten single-digit numbers (0 through 9), a hexadecimal system has sixteen single-digit numbers. These are the sixteen single-digit numbers of the hexadecimal system:

  • 0, 1 , 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Because there are only so many single-digit numbers in math, the system uses some letters as numbers. In the hexadecimal system:

  • A is 10
  • B is 11
  • C is 12
  • D is 13
  • E is 14
  • F is 15

Hexadecimal Place Values

The number system we use every day is base-ten, and its place values are the ones column, tens column (which represents the numeral x 10), hundreds column (which represents the numeral x 10 x 10), and so on. After the ones place, each place value increases by the power of 10.

Place values of the base-ten system (on the left) and the hexadecimal system (on the right)

In the hexadecimal (base-sixteen) system, there are also place values, but they are different. It starts with the ones, and each place value increases by the power of 16. So, there's a ones column, a sixteens column (which represents the numeral x 16), a two-hundred-and-fifty-sixes column (which represents the numeral x 16 x 16), and so on.

Comparing Base-Ten and Base-Sixteen Place Values

Let's use the number 17 to compare the base-ten system and the hexadecimal (base-sixteen) system.

The left chart shows 17 on the base-ten system, and the right chart shows 17 on the base-sixteen system.

Take a look at the base-ten chart. In the ones place, you can only go up to 9. After that--to represent a ten--you have to move over to the tens place. So, to show 17, you make one mark in the tens place column and seven marks in the ones place column.

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