Decimal to Hex Converter
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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 1E7B16 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.