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Subtraction of Octal Numbers

The subtraction of octal numbers follows the same rules as the subtraction of numbers in any other number system. The only variation is in the quantity of the borrow. In the decimal system, you had to borrow a group of 10₁₀. In the binary system, you borrowed a group of 2₁₀. In the octal system you will borrow a group of 8₁₀.

Consider the subtraction of 1 from 10 in decimal, binary, and octal number systems:

In each example, you cannot subtract 1 from 0 and have a positive difference. You must use a borrow from the next column of numbers. Let's examine the above problems and show the borrow as a decimal quantity for clarity:

When you use the borrow, the column you borrow from is reduced by 1, and the amount of the borrow is added to the column of the minuend being subtracted. The following examples show this procedure:

In the octal example 7₈ cannot be subtracted from 6₈, so you must borrow from the 4. Reduce the 4 by 1 and add 10₈ (the borrow) to the 6₈ in the minuend. By subtracting 7₈ from 16₈, you get a difference of 7₈. Write this number in the difference line and bring down the 3. You may need to refer to table 1-4, the octal addition table, until you are familiar with octal numbers. To use the table for subtraction, follow these directions. Locate the subtrahend in column Y. Now find where this line intersects with the minuend in area Z. The remainder, or difference, will be in row X directly above this point.

Do the following problems to practice your octal subtraction:

Q.30 Subtract:

Q.31 Subtract:

Q.32 Subtract:

Q.33 Subtract:

Q.34 Subtract:

Q.35 Subtract: