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Converting DECIMAL to HEXIDECIMAL and vice versa

Converting a decimal number to its hex representative is relatively easy. I will demonstate one method for each conversion. Hex is referred to as base16, a numeral system that uses 16 symbols. The symbols available to us are: 1-9 and A-F. This can be broken out into the following representations (hex on the left, decimal on the right):

DECIMAL to HEX Example 1

Lets pick a decimal number, 1009.

Divide the number by 16.

1009 / 16 = 63.0625 (disregard everything after the decimal point) = 63

Now times the remainder 0.0625 by 16.

0.0625 * 16 = 1

Note the answer 1.

Now take division result of 63 and divide this by 16.

63 / 16 = 3.9375 (disregard everything after the decimal point) = 3

Now times the remainder 0.9375 by 16.

0.9375 * 16 = 15.

Note the answer 15 (15 = F)

Now take division result of 3 and divide this by 16.

3 / 16 = 0.1875 (disregard everything after the decimal point) = 0

When we hit 0 on the division, we have reached the end of the chain. Record 3 as the final conversion.

The final step is to simply put the remainders and final conversion together:

3F1

Its always worth checking your conversion using an online decimal to hex tool to ensure your answer is correct.

DECIMAL to HEX Example 2

My decimal number is 54.

54 / 16 = 3.375 = 3


                    0.375 * 16 = 6 (1st number)



                    3 / 16 = 0.1875 (note the 3 (2nd number) as this is the end of the chain)



                    DEC 54 = HEX 36

DECIMAL to HEX Example 3

My decimal number is 633.

633 / 16 = 39.5625 = 39


                    0.5625 * 16 = 9 (1st number)



                    39 / 16 = 2.4375 = 2


                    0.4375 * 16 = 7 (2nd number)



                    2 / 16 = 0.125 = 2 (3rd number)



                    DEC 633 = HEX 279

DECIMAL to HEX Example 4

My decimal number is 256.

256 / 16 = 16.0


                    0 * 16 = 0 (1st number)



                    16 / 16 = 1.0 = 2


                    0 * 16 = 0 (2nd number)



                    1 / 16 = 0.0.625 = 1 (3rd number)



                    DEC 256 = HEX 100

HEX to DECIMAL Example 1

Converting from hex to decimal is again relatively straight forward, a calculator will again come in handy!

Choose a hex number, I will use A7F.

Follow this simple rule, reading the hex numbers from left to right:


                    A = 10

                    10 * 16^2 = 2560


                    7 = 7

                    7 * 16^1 = 112


                    F = 15

                    15 * 16^0 = 15


                    2560 + 112 + 15 = 2687


                    HEX A7F = DEC 2687

HEX to DECIMAL Example 2

My hex number is F6F1


                    F = 15

                    15 * 16^3 = 61440



                    6 = 6

                    6 * 16^2 = 1536



                    F = 15

                    15 * 16^1 = 240



                    1 = 1

                    1 * 16^0 = 1



                    61440 + 1536 + 240 + 1 = 63217


                    HEX F6F1 = DEC 63217

HEX to DECIMAL Example 3

My hex number is F1


                    F = 15

                    15 * 16^1 = 240



                    1 = 1

                    1 * 16^0 = 1




                    240 + 1 = 241


                    HEX F1 = DEC 241

Hopefully that all makes sense, if not ping me an email and I will try to explain further.

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