Q:

# How do you subtract hexadecimal numbers?

A:

Subtracting hexadecimal numbers is not much different than subtracting decimal numbers once you understand what a hexadecimal number is. The hexadecimal system is based on the number 16 instead of the number 10 like the familiar decimal system.

## Keep Learning

1. Understand how to count with hexadecimal numbers

Just as the decimal system has 10 digits, 0 through 9, the hexadecimal system has 16 digits. The 16 digits of hexadecimal are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.

2. Convert hexadecimal letters into decimal equivalents

When doing operations such as subtraction with hexadecimal numbers, think of the letters as equal to numbers, so A equals 10, B equals 11, C equals 12, D equals 13, E equals 14 and F equals 15.

3. Line up numbers with more than one place, and subtract from right to left

For a problem with more than one digit, line the two numbers up just as in decimal subtraction, aligning the placeholder positions. For example, FF minus D1 is aligned into F minus 1 and F minus D. As with decimal subtraction problems, begin at the right. F minus 1 is the same as 15 minus 1 which equals 14, or E in the hexadecimal system. F minus D is the same as 15 minus 13, which equals 2. Therefore, FF minus D1 equals 2E.

4. Borrow 16 from the next higher place when necessary

In decimal subtraction, when the number to be subtracted is greater than the number to be subtracted from, you solve by borrowing a 10 from the next higher place. In hexadecimal subtraction, you borrow a 16 instead. So for 26 minus 18, because 8 is greater than 6, you must borrow a 16 from the 2. Add the 16 to the 6. This gives you 22, from which the 8 is subtracted to equal 14, or E. Since you borrowed from the higher position, only 1 is left from which to subtract 1. In other words, 26 minus 18 is equal to E in the hexadecimal system, not 8 as it is in decimal.

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