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A gentle (smile) introduction to hexadecimal (base 16).

Table of Contents

Decimal numbers

In our standard decimal system each digit (which can be 0,1,2,3,4,5,6,7,8,9) in a number represents a power of ten in that place:

Hexadecimal numbers

The hexidecimal (base 16) system is similar, except that each digit represents a power of 16 in that place.


To convert a decimal number to hex, you remove multiples of those powers of 16 as shown below.

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Binary numbers

In the binary (base 2) system, each digit is a power of two, and the digits are just 0 and 1.

It's easy to translate a hexadecimal number into binary because you can decompose each hex digit into its 4 bits.

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The benefit of using hexadecimal instead of binary, is that it hex is much shorter to write, but still lets us easily determine the value of specific bits:Image Removed.

Octal numbers

Another popular base in the computer world is octal – (base 8) where each digit is a power of 8, and digits are 0, 1, 2, 3, 4, 5, 6, 7.

Octal is more compact than binary, but less compact than either decimal or hexadecimal.