Tutorial: Hexadecimal

Numbering Systems (Third of Four Parts: Hex)

Number system based on 16
  • 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
  • Powers of 16

The hexadecimal number system is exactly the same as the decimal and binary number systems, except it is based on sixteen instead of ten or two. You could even call it base 16 arithmetic if you wanted to.

There are sixteen symbols in the hexadecimal number system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Note that we use the letters A, B, C, D, E and F as symbols to represent the quantities 10, 11, 12, 13, 14 and 15 respectively, since symbols can have only one character. Quantities are represented in hexadecimal as powers of sixteen.

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Number Systems (Third of Four Parts: Hexadecimal)

Just as in decimal and binary, when expressing quantities in hexadecimal, we use a shorthand notation. This indicates how many of which powers of sixteen are needed to make up the quantity.

For example, when we write the number "7C9H", what we mean is 7 x 162 + 12 x 161 + 9 x 160 .

This could also be written as (7 x 256) + (12 x 16) + (9 x 1) .

The hexadecimal symbols 7, C and 9 indicate, for the appropriate power of 16, how many of that power of sixteen go in to making up the quantity.

In other words, the numbers 7, C and 9 are placeholders in our shorthand notation, indicating how many of the powers of sixteen in that place go in to making up the quantity.

Compare this to our understanding of decimal numbers, and you will see that the concept of binary, decimal and hexadecimal are all the same - only the base is different. Hexadecimal is based on sixteen; decimal is based on ten and binary is based on two.

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