7. Hexadecimal numbers

This is name given to numbers using the base-16 notation.

Allowed Hexadecial digits are:

The decimal numbers 10 to 15 are represented with the letters A to F. There are 16 values, hence why it is a base-16 number system.

Hexadecimal is widely used in computing because it is a much shorter way of representing a byte of data. If we were to represent a byte of data in binary, it would require 8 digits, e.g. 11111111.

However, that same byte of data could be represented in hexadecimal in just two digits e.g. FF - much more compact and user friendly than a binary number.

The table above only shows hexadecimal numbers up to denary 15. The largest byte value is 255 and you can use hexadecimal numbers to represent up to this value.

We can extend the table above to show the next set of hexadecimal numbers:

Once we have gone past the first 16 numbers, a 1 is added in front of the next 16 numbers (similar to denary when we go from 0-9 and then the next 10 numbers have a 1 in front of them)

The next set of hexadecimal numbers would have a 2 in front of them:

See if you can complete the table for the next set:

Hex Decimal Calculator
0F 15 decimal
10 16 decimal (1x16)
20 32 decimal (2x16)
30 48 decimal (3x16)
40 64 decimal (4x16)
50 80 decimal (5x16)
60 96 decimal (6x16)
70 112 decimal (7x16)
80 128 decimal (8x16)
90 144 decimal (9x16)
A0 160 decimal (10x16)

As you can see, the second digit in a hex number is multiplied by 16 to work out the decimal equivalent so the 4 x 16 = 64