Hexadecimal subtraction explained simply

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The hexadecimal system is a 16-digit place value system that is particularly popular in the IT sector. With a little training, however, dealing with the number system is not difficult at all. The following post demonstrates how to subtract two hexadecimal numbers.

The hexadecimal system, like the decimal system that you use in everyday life, is a place value system. This means that the value of a hexadecimal number, like the value of a decimal number, results from the value of the individual digits and from where they are in the number. As an example, here are the two Decimal numbers 80 and 800 where you can clearly see how where a digit is placed affects the value of the number.

In the hexadecimal system, however, you work with the base 16 and not with the base 10, which means that you will find 16 different digits in the hexadecimal system. Since there are basically only the 10 digits 0-9 known from the decimal system, one uses for the In the hexadecimal system, the letters A-F are also used, so that the values ​​10-15 are also used for a digit in a hexadecimal number to be able to express.

Subtraction in the decimal system: how to proceed

  • Since the hexadecimal system, like the decimal system, is a place value system, it works Addition and subtraction of hexadecimal numbers in principle as you would with the decimal system familiar with.
  • As in the decimal system, in the hexadecimal system you drag the values ​​of the digits in the same places of the Counting as subtrahends and minuends and note the difference as the corresponding digit of the result. Proceed from right to left.
  • If the minuend is greater than the subtrahend, you also create a carry of 1 in the next higher position.
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Example of subtraction in the hexadecimal system

As an example, the two hexadecimal numbers 2E9A (decimal 11930) and 12F7 (decimal 4855) should be subtracted from each other:

  1. First, subtract the two digits furthest to the right in the numbers, i.e. A -7 = 3.
  2. Then follow the digits 9 and F, whereby you get the result 9 - F = A carry-over 1.
  3. Then subtract E and 3 (instead of 2, because of the carry), which results in E - 3 = B.
  4. Finally, subtract the digits 2 and 1 and get the result 2 - 1 = 1.
  5. The overall result is then 1BA3, which in decimal notation results in 7075.
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