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A gentle 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.

Because a digit can have values greater than 9, there are additional digit values symbols allowed in hex:

  • A (10), B (11), C (12), D (13), E (14) and F (15)

...

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

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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.

Because 16 is a power of 2 (2^4), every hex digit corresponds to a set of 4 binary digits ("bits"), with each digit representing a power of 2:

decimalhexbinary
000000
110001
220010
330011
440100
550101
660110
770111
881000
991001
10A1010
11B1011
12C1100
13D1101
14E1110
15F1111

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.

Since 8 is also a power of 2 (2^3), each octal digit corresponds directly to 3 binary bits. So octal is more compact than binary, but less compact than either decimal or hexadecimal.