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Number Systems: Base 16 Hexadecimal

Document Reference: TN200901005 - Rev: 4.18 - Last Update: 21-03-2014 22:23 GMT - Downloaded: 24-Jul-2019 13:38 GMT

The hexadecimal (aka Base 16) number system uses sixteen symbols for counting and expressing value.

Hexadecimal Symbols and Values

In the hexadecimal number system, the symbols 0 to 9 represent values zero to nine and the symbols A to ?F (or lower case a to f) represent the values greater than 9 (ten to fifteen). Hexadecimal values are usually represented by the subscript '16', subscript 'hex', subscript 'h', the following letter 'H' or preceding '0x'.

Hexadecimal Symbols Table

Decimal ValueHexadecimal SymbolPossible Hexadecimal Value Representations
00016      or      0hex      or      0h      or      0H      or      0x0
11116      or      1hex      or      1h      or      1H      or      0x1
22216      or      2hex      or      2h      or      2H      or      0x2
33316      or      3hex      or      3h      or      3H      or      0x3
44416      or      4hex      or      4h      or      4H      or      0x4
55516      or      5hex      or      5h      or      5H      or      0x5
66616      or      6hex      or      6h      or      6H      or      0x6
77716      or      7hex      or      7h      or      7H      or      0x7
88816      or      8hex      or      8h      or      8H      or      0x8
99916      or      9hex      or      9h      or      9H      or      0x9
10AA16      or      Ahex      or      Ah      or      AH      or      0xA
11BB16      or      Bhex      or      Bh      or      BH      or      0xB
12CC16      or      Chex      or      Ch      or      CH      or      0xC
13DD16      or      Dhex      or      Dh      or      DH      or      0xD
14EE16      or      Ehex      or      Eh      or      EH      or      0xE
15FF16      or      Fhex      or      Fh      or      FH      or      0xF

Hexadecimal Digits

Similar to the base 10 system, the left most digit within a hexadecimal number is the least significant digit (LSD) and has the lowest place value. As further the digits move to the right, as higher the place value becomes. The right most digit within a hexadecimal number is the most significant digit (MSD) and has the highest place value.

Hexadecimal Place Values

6. Digit
From Left
5. Digit
From Left
4. Digit
From Left
3. Digit
From Left
2. Digit
From Left
Left Most
Digit
Power of 16 (16x):165164163162161160
Place Value:1048576106553610409610256101610110

Place values are shown in decimal (base 10) number system as this is the number system we are most familiar with.

Hexadecimal Number Line

Example of a number line displaying hexadecimal numbers from -116 to 1B16 only:

Hexadecimal Number Line

The subscript '16' is not required as the number line is labelled 'Hexadecimal Number Line' and is omitted for clarity.

Hexadecimal Counting

Hexadecimal Counting Example

Counting Bananas in Hexadecimal

In above image, let us count all the bananas in hexadecimal. We count as follows:

1 … 2 … 3 … 4 … 5 … 6 … 7 … 8 … That's it, there are 816 bananas in above image!

Counting Pears in Hexadecimal

Now let us count all the pears in hexadecimal. We count as follows:

1 … 2 … 3 … 4 … 5 … 6 … 7 … 8 … 9 … A … B … C … D … E … F … 10 … 11 … 12 … 13 … That's it, there are 1316 pears in above image! Remember not to say thirteen, as this would be the decimal pronunciation. Call the number digit by digit, e.g. one – three hexadecimal.

Counting Apples in Hexadecimal

We can also count all the apples in hexadecimal. We count as follows:

1 … 2 … 3 … 4 … 5 … 6 … 7 … 8 … 9 … A … B … C … D … E … F … 10 … 11 … 12 … 13 … 14 … 15 … 16 … 17 … 18 … 19 … 1A … 1B … 1C … 1D … 1E … 1F … 20 … 21 … 22 … 23 … 24 … 25 … That's it, there are 2516 apples in above image! Again remember not to say twenty-five, as this would be the decimal pronunciation. Call the number digit by digit, e.g. two – five hexadecimal.

Counting All Pieces of Fruit in Hexadecimal

Finally we count all the pieces of fruit in hexadecimal, count as follows:

1 … 2 … 3 … 4 … 5 … 6 … 7 … 8 … 9 … A … B … C … D … E … F … 10 … 11 … 12 … 13 … 14 … 15 … 16 … 17 … 18 … 19 … 1A … 1B … 1C … 1D … 1E … 1F … 20 … 21 … 22 … 23 … 24 … 25 … 26 … 27 … 28 … 29 … 2A … 2B … 2C … 2D … 2E … 2F … 30 … 31 … 32 … 33 … 34 … 35 … 36 … 37 … 38 … 39 … 3A … 3B … 3C … 3D … 3E … 3F … 40 … That's it, there are a total of 4016 pieces of fruit in above image! Don't say forty, just call it e.g. four – zero hexadecimal.

Hexadecimal Numbers in Computing

The primary use of the hexadecimal number system is a human-friendly representation of binary-coded values in computing and digital electronics where one hexadecimal digit represents four binary digits.

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