## 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):

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

## 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`

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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