Hexadecimal Conversion

Hexadecimal(hex) to Decimal(Dec) Converter

Enter your hexadecimal or Decimal number below and hit the appropriate button to convert the number as you desire.

To Decimal
To Hexadecimal
This is the answer box

Hexadecimal is base 16.

Base 16 is where the 'numbers' you can use are zero through to the letter F (0123456789ABCDEF). i.e. the decimal value for '1' is represented in hexadecimal as '1' but the hexadecimal value of '15' (decimal) is shown as 'F' (hexadecimal) and the value of '17' (decimal) is '11' in Hexadecimal.

DecimalHex DecimalHex DecimalHex

Example of converting Decimal 234 into Hexadecimal

Note I'm using the subscript NNNNhex to represent Hexadecimal numbers, across the web you' see other styles too e.g. 0xNNNN or NNNN16 , all are valid.

Decimal Units

First let's go back to decimal and remind ourselves how that works as the two systems have much in common.

We are looking at the decimal number 234, let's break that into its decimal units.

234 has 3 units. Hundreds, tens and single units.

2 x 100 (hundreds)

3 x 10 (tens)

4 x 1 (units)

Of course if we add these up it will give us the original 234

Hexadecimal Units

The Hexadecimal version of 234 is 'ea', let's do the same with that

ea has 2 units 16's and single units.

e x 16

a x 1

Add these up and we still get the answer 234!

But why have the units changed?

Consider the following chart, this is how the first 16 characters of Hexadecimal work.

1 in decimal is1 in hexadecimal.
2is 2
3is 3
4is 4
5is 5
6is 6
7is 7
8is 8
9is 9
10is a
11is b
12is c
13is d
14is e
15is f
16is 10

This means when we get to Hex "10" we've already been able to represent 16 numbers. In fact we've run out of numerals and have to start using letters of the alphabet. - Hex uses the first 6 letters "a" thru "f" for the numbers 10 thru 15. So it follows that the second unit in hex is now worth 16, the third unit is now worth 256, the forth 4096 and so on, with each unit increasing by a factor of 16. So it's common (and indeed has happened in our case) for the hex number to use less characters to represent the same value. So to recap, 234 in decimal is eahex in hexadecimal.

... and broken down our number eahex looks like this;

e x 16 = 224 (e is 14)

a x 1 = 10 (a is 10)

total = 234 Yay!!!

Example of converting 234 Hexadecimal into Decimal

The answer to the question (what is Decimal for 234 in hex ?) is 564.

As before I'm using the subscript NNNNhex to represent Hexadecimal numbers. Across the web you' see other styles too e.g. 0xNNNN or NNNN16, all are valid.

With the previous example we looked at the units of the numbers and we'll do that again here.

5 x 100 (hundreds)

6 x 10 (tens)

4 x 1 (units)

This shows the answer and how it's split into decimal units.

Now let's look at our hexadecimal number 234, and break that into it's units.

234hex has 3 units.

2 x 256

3 x 16

4 x 1

Of course if we add these up it will give us the decimal 564 This is basically how we calculate decimal from hexadecimal.

To recap, 234hex in hexadecimal is 564 in decimal.

... and broken down our number 234hex looks like this;

2 x 256 = 512

3 x 16 = 48

4 x 1 = 4

total = 564 Yay!!

If there are any problems with the above page please let me know, or if you'd like to suggest an improvement I'm more than happy to include it.