# Decimal to Hex Converter

**convert a decimal to a hex value**. Decimal is a number system made up of 10 symbols (base 10). Hex is made up of 16 symbols (base 16). More information is available here.

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## Decimal and Hex(adecimal)

Decimals are numbers as we use them in our daily lives; whole numbers, like those used for counting items. Decimal is called **base 10**, because it uses 10 distinct numbers to count.

i.e. **0, 1, 2, 3, 4, 5, 6, 7, 8, 9.**

Hex numbers, or "hexadecimal", to use its full name, is **base 16**. It uses 16 distinct characters to count.

i.e. **0, 1, 2, 3, 4, 5, 6, 7, 8, 9,** plus the letters **A, B, C, D, E, F.**

Putting these numbers side by side, we can get an idea of how to convert the most basic of decimal numbers to hex:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 A B C D E F

Seeing decimal and hex numbers together like this, we can easily see that **10** in decimal is the same as **A** in hex, and **15** in decimal is **F** in hex.

## How to convert from decimal to hex

- Divide the decimal by 16 until the result is 15 or less.
- Take the whole number (before the decimal point) and look up the corresponding hex value in the hex-decimal comparison list above (e.g. 10 = A, 15 = F).
- Take the remainder (after the decimal point) and multiply by 16.
- Repeat steps 2 and 3 with the result, until you're left with no remainder.

### Example of decimal to hex conversion

Let's take the decimal **7803**. First we **divide** it down by 16.

- 7803 ÷ 16 =
**487.6875**(result over 15, must divide again) - 487.6875 ÷ 16 =
**30.48046875**(result over 15, must divide again) - 30.48046875 ÷ 16 =
**1.9050293** - 0.9050293 x 16 = 14.4804688 (second decimal digit is
**14**) - 0.4804688 x 16 = 7.6875008 (third decimal digit is
**7**) - 0.6875008 x 16 = 11.0000128 (rounds to
**11**, our last decimal digit)

The first decimal digit is **1**. So now we begin **multiplying** the remainder by 16.

**So we have the resulting digits of 1-14-7-11.**

Using the hex-decimal comparison list above again, 1 and 7 are unchanged, while 14 is **E**, and 11 is **B**.

Putting them all together gives us **1E7B**. We can write it as **1E7B _{16}** to show that it's a hex number.

**Note:** Should you wish you convert your decimal to a fraction, give the decimal to fraction calculator a try.

If you have any problems using this decimal to hex calculator, please contact me.