Subtraction of Hex Numbers

The subtraction of hex numbers looks more difficult than it really is. In the preceding sections you learned all the rules for subtraction. Now you need only to apply those rules to a new number system. The symbols may be different and the amount of the borrow is different, but the rules remain the same.

Use the hex addition table (table 1-6) to follow the solution of the following problems:

Working from left to right, first locate the subtrahend (2) in column Y. Follow this line across area Z until you reach C. The difference is located in column X directly above the C - in this case A. Use this same procedure to reach the solution:

Now examine the following solutions:

In the previous example, when F was subtracted from 1E, a borrow was used. Since you cannot subtract F from E and have a positive difference, a borrow of 10₁₆ was taken from the next higher value column. The borrow was added to E, and the higher value column was reduced by 1.

The following example shows the use of the borrow in a more difficult problem:

In this first step, B cannot be subtracted from 7, so you take a borrow of 10₁₆ from the next higher value column. Add the borrow to the 7 in the minuend; then subtract (17₁₆ minus B₁₆ equals C₁₆). Reduce the number from which the borrow was taken (3) by 1.

To subtract 4₁₆ from 2₁₆ also requires a borrow, as shown below:

Borrow 10₁₆ from the A and reduce the minuend by 1. Add the borrow to the 2 and subtract 4₁₆ from 12₁₆. The difference is E.

When solved the problem looks like this:

Remember that the borrow is 10₁₆ not 10₁₀.

There may be times when you need to borrow from a column that has a 0 in the minuend. In that case, you borrow from the next highest value column, which will provide you with a value in the 0 column that you can borrow from.

To subtract A from 7, you must borrow. To borrow you must first borrow from the 2. The 0 becomes 10₁₆, which can give up a borrow. Reduce the 10₁₆ by 1 to provide a borrow for the 7. Reducing 10₁₆ by 1 equals F. Subtracting A₁₆ from 17₁₆ gives you D₁₆. Bring down the 1 and F for a difference of 1FD₁₆.

Now let's practice what we've learned by solving the following hex subtraction problems:

Q.42 Subtract:

Q.43 Subtract:

Q.44 Subtract:

Q.45 Subtract:

Q.46 Subtract:

Q.47 Subtract: