Conversion from Decimal to Hexadecimal

I want to share a little trick which some of you may not know for converting from Decimal to Hexadecimal as required for Computer Science GCSE and A Level. To use this trick, you will need to be able to convert from decimal to binary, which will be covered in another article.

When working with hexadecimal, it’s always a good idea to make a note of the values for the letters which represent the integers from 10-15:

A = 10, B = 11, C = 12, D = 13, E = 14, F = 15

Let’s look at an example. Say you want to convert the decimal number 168 into hexadecimal.

  • First, convert to binary using your preferred method. This gives

    • 10101000
  • Next split the binary number into nibbles like so:

    • 1010 1000

    • (If your binary number doesn’t consist of a multiple of 4 digits, add some zeros to the left-hand side to “pad” it.)

  • Then you convert your binary number into hexadecimal one nibble at a time:

    • 1010 in binary is 10 in decimal, which is A in hex.
    • 1000 in binary is 8 in decimal, which is 8 in hex.
  • And there it is – you have converted a decimal number into hexadecimal! 168 in decimal is A8 in hex.

The method works because the range of a binary nibble is 0000 to 1111, which is exactly the same range that one hexadecimal character can represent.

Get some practice by attempting to convert the following decimal numbers to hexadecimal using the “via binary” method.

(a) 64 (b) 254 (c) 181 (d) 256(e) 99

I hope that was helpful. Look out for more articles on data representation for Computer Science GCSE and A Level in the near future.

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