# Hexadecimal conversion calculator

Hexadecimal (sometimes just hex) is another way of representing numbers. Instead of using base 10 (decimal) or base 2 (binary), hexadecimal uses base 16. The decimal number system uses the symbols 0-9 to represent the ten decimal digits. For a base 16 number, six more symbols are needed, so the letters A-F are used as well. The table below shows the 16 hexadecimal digits and their decimal equivalents.

Hexadecimal is useful because each digit represents a group of four binary digits (also called a nybble). Binary numbers can be very long, so hexadecimal is used as a more people-friendly representation of binary numbers in computing.

How to convert

Look at this binary number: 0101110010101001.
This long number can be converted into a 4 digit hexadecimal number that is much more manageable.

The first step in converting this binary number to hexadecimal is to separate the digits into nybbles (groups of four): 0101 1100 1010 1001
Each nybble will become a single digit in the hexadecimal number.

Each digit within a nybble corresponds to a power of 2 – 23 (8), 22 (4), 21 (2) and 20 (1). If the digit in the nybble is 0 there are no lots of that number, but if the digit is 1 then you add that power to the total for the nybble (which will be a number less than 16).

Start with the first nybble: 0101

- The first digit is 0 so there are 0 lots of 8

- The second digit is 1 so there is 1 lot of 4

- The third digit is 0 so there are 0 lots of 2

- The fourth digit is 1 so there is 1 lot of 1

Adding these together (4 + 1) makes 5, so the first digit of the new hexadecimal number is 5.

The second nybble is: 1100

- The first digit is 1 so there is 1 lot of 8

- The second digit is 1 so there is 1 lot of 4

- The third digit is 0 so there are 0 lots of 2

- The fourth digit is 0 so there are 0 lots of 1

Adding these together (8 + 4) comes to 12, so the second digit of the hexadecimal number is C (see the conversion table above).

Convert the other two nybbles in this number to calculate a four digit hexadecimal number.

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Enhance your calculator

In your calculator you should have two nybbles, so you will be adding formulae to convert an eight digit binary number to a 2 digit hexadecimal number.

Open Binary to hexadecimal – Enhancing the calculator (.docx 27kB) for instructions to alter the Excel spreadsheet that you saved previously.