# Octal Number Subtraction

Octal number subtraction 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 10 base 10. In the binary system, you borrowed a group of 2 base 10. In the octal system you will borrow a group of 8 base 10.

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. Letâ€™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 7 base 8 cannot be subtracted from 6 base 8, so you must borrow from the 4. Reduce the 4 by 1 and add 10 base 8 (the borrow) to the 6 base 8 in the minuend. By subtracting 7 base 8 from 16 base 8, you get a difference of 7 base 8.

Write this number in the difference line and bring down the 3. You may need to refer to table for octal addition in the previous tutorial on octal addition, 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.