Sep 22, 2021 2 min read

# Hexadecimal number system

In this article, I will describe how you can convert from Denary - Binary - Hexadecimal. The Hex (Hexidecimal) number system is used for web colour codes, MAC addresses, and error codes in computer systems.

The Hex number system is similar to the binary system, it's a base 16 system and needs to use 16 digits to represent each value.

The 16 digits are made up of 1 - 9 and A - F are used to represent each Hex value. 10 in denary = A in Hex, 11 = B, 12 = C, 13 = D, 14 = E and 15 = F

Since 16 = 2 4, every four binary digits are equivalent to one Hex digit.

The table above shows the equivalent values for each number system, the following sheet shows the steps used to convert the denary value 142 which we convert to Binary and then Hex by splitting the binary number into 4 bits, we then use the Binary number system 8421 to calculate each value and then add them together. 142 is 10001110 in Binary, we then split this into two 4 bit values 1000 and 1110 using our Binary number system 8421 gives us 8 + 14 - 14 in Hex = E so the Hex equivalent of 142 = 8E.

If we want to convert a Binary value to Hex we can use the same system, for example, 10011101110 we split into 4-bit values which will give us:

0100 1110 1110 I have added an extra 0 to the start so we have 4 values - technically you don't need to add the 0 as the value will remain the same.

4 14 14, 14 in Hex = E so 10011101110 in Hex = 4EE with this method of converting you only need to be able to add 8421 values to carry out your calculations, this will work for any value in Denary or Binary, it can also be used in reverse to convert Hex to Denary. Self-taught techie, with a passion for computers and all the cool things you can do with them. Techie Mike, B.Eng. B.Sc.
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